Full of beans: a study on the alignment of two flowering
                  plants classification systems

                         Yi-Yun Cheng and Bertram Ludäscher

      School of Information Sciences, University of Illinois at Urbana-Champaign, USA
                      {yiyunyc2,ludaesch}@illinois.edu



       Abstract. Advancements in technologies such as DNA analysis have given rise
       to new ways in organizing organisms in biodiversity classification systems. In
       this paper, we examine the feasibility of aligning two classification systems for
       flowering plants using a logic-based, Region Connection Calculus (RCC-5) ap-
       proach. The older “Cronquist system” (1981) classifies plants using their mor-
       phological features, while the more recent Angiosperm Phylogeny Group IV
       (APG IV) (2016) system classifies based on many new methods including ge-
       nome-level analysis. In our approach, we align pairwise concepts X and Y from
       two taxonomies using five basic set relations: congruence (X=Y), inclusion
       (X>Y), inverse inclusion (X<Y), overlap (X><Y), and disjointness (X!Y). With
       some of the RCC-5 relationships among the Fabaceae family (beans family) and
       the Sapindaceae family (maple family) uncertain, we anticipate that the merging
       of the two classification systems will lead to numerous merged solutions, so-
       called possible worlds. Our research demonstrates how logic-based alignment
       with ambiguities can lead to multiple merged solutions, which would not have
       been feasible when aligning taxonomies, classifications, or other knowledge or-
       ganization systems (KOS) manually. We believe that this work can introduce a
       novel approach for aligning KOS, where merged possible worlds can serve as a
       minimum viable product for engaging domain experts in the loop.

       Keywords: taxonomy alignment, KOS alignment, interoperability


1      Introduction
With the advent of large-scale technologies and datasets, it has become increasingly
difficult to organize information using a stable unitary classification scheme over time.
An ideal work classification system, as noted in [1], should be neither too fine-grained,
nor too esoteric, to stand the test of time. However, a real-life knowledge organization
system (KOS) oftentimes has trade-offs in its stability and granularity, especially when
new developments have been made technologically. For example, the use of DNA anal-
ysis has provided new data signals that in turn have changed the way biologists classify
organisms—traditionally, they may classify organisms based on similarities of surface-
level features, while classifying based on similarities in micro-level DNA analysis has
become prevalent now. Therefore, the interoperability among different KOSs over time
2

addressing the same topic has become more and more important in this current era with
rapid developments and innovations.
    In the biodiversity communities, taxonomies, a type of KOS under the classification
schemes [2], has always been one of the main focuses of research; especially in the
field of systematics. As such, similar arguments about maintaining a ‘unitary classifi-
cation’ over time were made in [3]. The authors [3] stated that it is common for taxon-
omists to contradict each other’s or even their own previous taxonomies. To this end,
rather than having a permanent anchor for a specific KOS (taxonomy or classification
scheme), a better approach, perhaps, is to embrace the fact that KOS are dynamic, time-
specific, and responsive to both empirical signals and human classification interests.
Thus, a more principled solution in dealing with the interoperability issues among KOS
is perhaps to compare and align the classifications and at the same time presenting the
disagreements among them [3][4].
    In this paper, we propose the use of a logic-based approach to compare and recon-
cile two major classification systems in the field of plant systematics, with the aim of
demonstrating the feasibility of integrating two classifications that result in numerous
possible solutions. Further, we demonstrate the computational power that can aid us in
aligning KOS which could not have been possible when working with alignments man-
ually. Specifically, we consider a use case of the flowering plants classification systems
by (1) Arthur Cronquist (1981) [5], and (2) Angiosperm Phylogeny Group IV [6] in
order to map plant families (concepts) mentioned in both classifications with one of the
five Region Connection Calculus relations (RCC-5) using an open source, logic-based
tool named Euler/X. The flowering plants we have included in this study are not only
some of the most common families that we see in our everyday lives, such as the sun-
flowers (Asteraceae sec. APG IV1), but also those flowering plants by a biologist’s
definition such as the beans family (Fabaceae sec. APG IV). We hope that this work
will further shed light on the possible alignments of the classifications in the infor-
mation science community and bring a novel approach for aligning KOS in the future.


2         Two Flowering Plant Classifications
In line with the traditions of Bentham and Hooker, Takhtajan, and Bessy, the Cronquist
system [5] is an approach in classifying and identifying flowering plants based on phy-
letics (classifying resemblances based on evolution and morphological similarity - sim-
ilar characters - of the plants). The Cronquist system divides the whole flowering plant
world into two phyla, Magnoliopsida and Liliopsida, with approximately 300 families
included in the former, and 60 families in the latter [5]; this system is said to be the
most “fully developed phyletic system” of flowering plant classification systems2 by
far [7][8].
   However, rapid breakthroughs in DNA studies and technologies have given rise to
a more recent camp of approaches in classifying plants based on phylogenetics. Early

1
    Taxonomic Concept Labels (TCLs): name sec. source
2
    In biodiversity classification systems, the sequence of the concepts is not taken into account.
                                                                                                                    3

cladistic analysis or phylogenetic systematics, established by Willi Hennig, has put sys-
tematics to the task of finding shared, derived character states among any three groups
of organisms to find their common ancestors, or clades [9]. Modern phylogenetics con-
sists of the use of “both morphological and molecular data and modern methods of data
analyses to study evolutionary relationships among organisms” [7]. The Angiosperm
Phylogeny Group system (APG IV) [6], is one classification in this camp that has be-
come the de facto standard for the classification of plants of the modern era. The most
noticeable differences between the APG IV system and the other plant classification
systems are in the higher-level ranks. Instead of using classes or phyla, the APG uses
clades (e.g. rosid clade, asterid clade), or even other higher-level ranks (e.g. monocots,
eudicots) [6]. Though the APG IV system has become the most recent major classifi-
cation systems, the Cronquist system, established almost 40 years ago, still remains
highly influential to this date for its completeness and comprehensiveness, and many
legacy papers with key plant data still used Cronquist’s classifications.


3      Reasoning about taxonomies and Euler/X
Taxonomies are one type of KOS with hierarchical structures, similar to classification
schemes [2]. Taxonomy alignment refers to the mapping and reconciliation of two or
more taxonomies. In our approach, we employ a logic-based approach called Region
Connection Calculus (RCC-5) to align concepts across taxonomies using five possible
relationships: congruence (X=Y), inclusion (X>Y), inverse inclusion (X<Y), overlap
(X><Y), and disjointness (X!Y). Euler/X (https://github.com/EulerProject/EulerX) is a
logic-based reasoning tool for taxonomy alignment based on set constraints, specifi-
cally RCC-5 and implemented in answer set programming and direct RCC reasoning.
                          =
                T1.a           T2.x
                                                                       T1.b                        T1.b
                                                                       T2.y        Nodes           T2.z          Nodes
                                                      T1.a                        T1.a
                                                      T2.x                        T2.x
                                                                       T1.c      congruent 3       T1.c       congruent 3
         T1.b     T1.c        T2.y    T2.z                             T2.z                        T2.y
                                                                                    Edges                        Edges

                 Input Taxonomies                                  PW1           is_a (input)PW2
                                                                                              2               is_a (input) 2

                                                 Nodes                                      Nodes

                   T2.z       T1.c            congruent T2.z 1            T1.b           congruent        1
        T1.a                           T1.a       T2               2                        T2 T2.y       2
        T2.x                           T2.x
                                                  T1               2                         T1           2
                   T1.b       T2.y                          T1.c          T2.y
                                                Edges                                       Edges
                                                                                                T1.c
                                       overlaps (inferred) 1                      T1.a
                                                                                    overlaps (inferred)   1
                       PW3                               PW5                      T2.x                              Nodes
                                         is_a Nodes
                                              (inferred)           2                        Nodes
                                                                                       is_a (inferred)
                                                                                                  T2.z    2
                                                                                                                  congruent      1
                                             is_a (input)
                                             congruent        2                          is_a (input)     2
                   T2.y       T1.c                       T2.y 1           T1.b            congruent       1          T2          2
       T1.a                            T1.a      T2                2                         T2 T1.b      2          T1          2
       T2.x                            T2.x
                                                 T1                2                         T1           2         Edges
                   T1.b       T2.z                          T1.c          T2.z
                                                Edges                                       Edges
                                                                                                                 is_a (input)    4
                                         is_a (inferred)           2                 overlaps (inferred) 1
                       PW4                                   PW6                           PW7                overlaps (inferred) 4
                                             is_a (input)          2                   is_a (inferred)    2
                                       overlaps (inferred) 1                            is_a (input)      2
      Fig. 1. A simple taxonomy alignment problem with T1, T2 and 7 possible worlds
4

   Given two taxonomies T1 and T2, and a set of articulations (relationships between
concept X in T1 and concept Y in T2, defined in RCC-5 relations), the Taxonomy Align-
ment Problem (TAP) is to derive a merged taxonomy T3. A TAP may have zero, one,
or many solutions – inconsistent, unique, or ambiguous solutions respectively. In pre-
vious work [4], we have addressed the challenges of vocabulary confusion and interop-
erability between similar but different taxonomies by reconciling the taxonomic disa-
greement via unique Euler/X solutions, i.e., where there is only one “possible world”
that includes all logically inferred inter-taxonomy relationships. In this paper, we fur-
ther demonstrate features of Euler/X, i.e., its capability to naturally represent ambiguity
via multiple possible worlds. A possible world is a consistent solution where there are
no contradictions on the ways concepts were aligned, and that each concept in the two
taxonomies is “sorted out” with exactly one of the five RCC relations. To show a simple
TAP example and the multiple possible worlds that exist, consider two taxonomies T1
and T2, each with two children (Figure 1). Assume that we only know about these that
the highest-level nodes are congruent to each other (T1.a == T 2.x); how T1.b, T1.c relate
to T2.y, T2.z is unknown. With these underspecified articulations in our TAP, ambigui-
ties arise. Therefore, we end up with seven possible worlds where PW1 and PW2 depict
how the concepts can be aligned congruently, PW3 to PW6 depict similar but subtle
differences on how T1.b, T1.c is included in or includes T2.y, T2.z, while PW7 depicts
T1.b, T1.c, T2.y, T2.z all overlapping each other (red dashed lines).


4      Method
It is well-known that the basic taxonomic ranks in biological classification include king-
dom, phylum, class, order, family, genus, and species. In this research, we are mainly
focusing on the alignment of the family-level flowering plants. Among the 295,383
flowering plants species [10] within the Magnoliophyta phylum sec. Cronquist, or the
Angiosperms sec. APG IV, we are considering only the 40 most common families or
subfamilies out of a total of 416 flower families [6]. These families include Magnoli-
aceae, Ranunculaceae, Papaveraceae, Cataceae, Betulaceae, Fabaceae, Rosaceae, just
to name a few.
    Both the Cronquist systems and the APG system have these 40 families or some
modifications to the names of these families in their classifications. Each family serves
as a concept in our alignment. In our first alignment study, if the family in both systems
shares the exact same name, we assume (possible incorrectly) that they are congruent
to each other. If there are similar but different names, we will leave the concepts un-
mapped at first. To be more specific, if concept X in the Cronquist system is exactly
the same as concept Y in the APG system, we will mark them as [C.X {=} APG.Y].
See Figure 2 for our initial input taxonomies. The following six articulations are the
ones that are uncertain to us because they have different names:
         [C.Caesalpiniaceae ? APG.Caesalpinioideae]
         [C.Mimosaceae ? APG.Mimosoideae]
         [C.Fabaceae ? APG.Faboideae]
         [C.Aceraceae ? APG.Sapindaceae]
         [C.Sapindaceae ? APG.Sapindaceae]
         [C.Hippocastanaceae ? APG.Sapindaceae]
                                                                                                                                                                                                                           =           APG.Poaceae
                                                                                                                                                                C.Cyperales                           C.Poaceae                                                               APG.Poales
                                                                                                                                             C.Commelinidae
                                                                                                                                                                                                      C.Araceae            =           APG.Araceae
                                                                                                                                                                 C.Arales                                                                                                   APG.Alismatales

                                                                                                                                               C.Arecidae       C.Arecales                           C.Arecaceae           =          APG.Arecaceae                          APG.Arecales
                                                                                                                             C.Liliopsida
                                                                                                                                                                                                                                                                                                                    APG.Monocots
                                                                                                                                                                                                                           =           APG.Liliaceae                          APG.Liliales
                                                                                                                                                                                                      C.Liliaceae

                                                                                                                                                C.Liliidae       C.Liliales                                                =
                                                                                                                                                                                                      C.Iridaceae                      APG.Iridaceae                        APG.Asparagales

                                                                                                                                                               C.Orchidales                                                =         APG.Orchidaceae
                                                                                                                                                                                                    C.Orchidaceae

                                                                                                                                                                                                                                                                =          APG.Magnoliaceae
                                                                                                                                                                                                                                      C.Magnoliaceae
                                                                                                                                                                                                    C.Magnoliales
                                                                                                                                                                                                                                                                                                                   APG.Magnoliales
                                                                                                                                                                                                                                      C.Papaveraceae            =          APG.Papaveraceae
                                                                                                                                                                                                    C.Papaverales
                                                                                                                                                               C.Magnoliidae
                                                                                                                                                                                                    C.Ranunculales                    C.Ranunculaceae           =         APG.Ranunculaceae                       APG.Ranunculales


                                                                                                                                                                                                                                        C.Lamiaceae             =           APG.Lamiaceae                                               APG.BasalEudicots
                                                                                                                                                                                                      C.Lamiales
                                                                                                                                                                                                                                                                =         APG.Scrophulariaceae                                                                 APG.Magnoliids
                                                                                                                                                                                                                                     C.Scrophulariaceae
                                                                                                                                                                                                                                                                                                                    APG.Lamiales
                                                                                                                                                                                                   C.Scrophulariales                    C.Oleaceae              =            APG.Oleaceae


                                                                                                                                                                                                                                     C.Asclepiadaceae           =
                                                                                                                                                                                                    C.Gentianales                                                         APG.Asclepiadaceae
                                                                                                                                                                                                                                                                                                                   APG.Gentianales
                                                                                                                                                                                                                                                                                                                                                                                               APG.Angiosperms
                                                                                                                                                                C.Asteridae                          C.Dipsacales                     C.Caprifoliaceae          =
                                                                                                                                                                                                                                                                           APG.Caprifoliaceae
                                                                                                                                                                                                                                                                                                                   APG.Dipsacales

                                                                                                                                                                                                     C.Solanales                       C.Solanaceae             =
                                                                                                                                                                                                                                                                            APG.Solanaceae                          APG.Solanales
                                                                                                                                                                                                                                                                                                                                         APG.AsteridClade
                                                                                                                                                                                                     C.Asterales                                                =                                                   APG.Asterales
                                                                                                                                                                                                                                       C.Asteraceae                         APG.Asteraceae


                                                                                                                                                                                                                                             =                                                    APG.Apiales
                                                                                                                                                                                                                                                           APG.Apiaceae
                                                                                                                                                                                                                       C.Apiaceae
                                                                                                                                                                                                                                                                                                                     APG.Ericales
                                                                                                                                                                                   C.Apiales                                                                    =            APG.Ericaceae
                                                                                                                                                                                                                                        C.Ericaceae                                                                                                                             APG.Eudicots

                                                                                                                                                                                                                                                                                                                                       APG.CaryophyllidClade
                                                                                                                                                                                                                                        C.Cactaceae             =           APG.Cactaceae
                                                                                                                                                                                                      C.Ericales


                                                                                                                                                                                                                                     C.Caryophyllaceae          =         APG.Caryophyllaceae                     APG.Caryophyllales
                                                                                                                                                                                                   C.Caryophyllales
                                                                                                                                                                                                                                      C.Portulacaceae           =          APG.Portulacaceae
                                                                              Nodes

                                                                                 C                  81                                                                                              C.Polygonales
                                                                                                                                                                                                                                      C.Polygonaceae            =          APG.Polygonaceae
                                                                           APG                      73
                                                                             Edges                       C.Magnoliophyta   C.Magnoliopsida                    C.Caryophyllidae                        C.Salicales
                                                                                                                                                                                                                                        C.Salicaceae            =
                                                                     is_a (C)                       80                                                                                                                                                                      APG.Salicaceae
                                                                                                                                                                                                      C.Violales
                                                               is_a (APG) 72
                                                                                                                                                                                                                                        C.Violaceae             =
                                                             articulations 41                                                                                                                        C.Capparales                                                            APG.Violaceae

                                                                                                                                                                                                                                      C.Cucurbitaceae           =                                                  APG.Malpighiales
                                                                                                                                                                                                      C.Malvales
                                                                                                                                                                                                                                                                           APG.Cucurbitaceae

                                                                                                                                                                                                                                       C.Brassicaceae           =                                                  APG.Cucurbitales




                            unknown on both sides (red dotted lines)
                                                                                                                                                                                 C.Euphorbiales                                                                            APG.Brassicaceae

                                                                                                                                                                                                                                      C.Euphorbiaceae           =
                                                                                                                                                                                                                                                                           APG.Euphorbiaceae
                                                                                                                                                                                                    C.Mimosaceae                                                                                                   APG.Brassicales
                                                                                                                                                                                                                           ?
                                                                                                                                                                                                                                        C.Malvaceae             =
                                                                                                                                               C.Rosidae         C.Fabales                           C.Fabaceae                                                             APG.Malvaceae                           APG.Malvales
                                                                                                                                                                                                                           ?         APG.Mimosoideae
                                                                                                                                                                                                                                                                                                                                         APG.RosidClade
                                                                                                                                                                                                  C.Caesalpiniaceae                                                                                                  APG.Fabales
                                                                                                                                                                                                                           ?          APG.Faboideae                          APG.Fabaceae

                                                                                                                                                                                                  C.Hippocastanaceae       ?        APG.Caesalpinioideae                                         APG.Sapindales
                                                                                                                                                               C.Sapindales

                                                                                                                                                                                                     C.Aceraceae           ?
                                                                                                                                                                                                                                     APG.Sapindaceae
                                                                                                                                                                                                                           ?

                                                                                                                                                                                                    C.Sapindaceae                                                                                 APG.Myrtales
                                                                                                                                                                C.Myrtales
                                                                                                                                                                                                                                      APG.Onagraceae
                                                                                                                                                                                                                           =
                                                                                                                                                                                                                                                                                                                                         APG.CoreEudicots
                                                                                                                                                                                                    C.Onagraceae                                                =           APG.Betulaceae                           APG.Fagales
                                                                                                                                                                                                                                        C.Betulaceae

                                                                                                                                                                                                                                                                =            APG.Fagaceae
                                                                                                                                                                                                                                        C.Fagaceae
                                                                                                                                                                                                      C.Fagales




 tems (green=Cronquist; yellow=APG), with the Fabaceae and the Sapinadaceae relationship
                                                                                                                                                                                                                                             =             APG.Rosaceae                                             APG.Rosales
                                                                                                                                                                                   C.Rosales                           C.Rosaceae




Fig. 2. Initial input taxonomies with six unknown relations, aligning the two classification sys-
                                                                                                                                                                                                                                                                                                                                                                                                                 5




                                                                                                                                                                                                                                                                =            APG.Moraceae
                                                                                                                                                              C.Hamamelidae                                                             C.Moraceae
                                                                                                                                                                                                      C.Urticales                                                                                                  APG.Saxifragales
                                                                                                                                                                                                                                                                =         APG.Hamamelidaceae
                                                                                                                                                                                                   C.Hamamelidales                   C.Hamamelidaceae

                                                                                                                                                                                                                                             =
6

    Due to the above six uncertain relationships, we expect that the articulations be-
tween the concepts of the two classifications in our initial input taxonomies are under-
specified and will result in numerous possible worlds. Furthermore, the bold assump-
tion to mark names that are spelled the same in both taxonomies as congruent is often
not enough, as noted in [12]. This is the reason we conducted a second round of align-
ment to seek out consultation from a domain expert to verify our ‘congruent’ align-
ments as well as to sort out the underspecified articulations. The possible worlds we
have produced in the first stage thus became the minimum viable product for us to com-
municate with the expert and let him/her grasp all possible solutions for the alignment
problem. The domain expert in our research asserted that the congruent alignments are
indeed correct and that the modified articulations for the Fabaceae and the Sapindaceae
families are as follows:
       [C.Caesalpiniaceae {=} APG.Caesalpinioideae]
       [C.Mimosaceae {=} APG.Mimosoideae]
       [C.Fabaceae {=} APG.Faboideae]
       [C.Aceraceae {<} APG.Sapindaceae]
       [C.Sapindaceae {<} APG.Sapindaceae]
       [C.Hippocastanaceae {<} APG.Sapindaceae]


5      Results
The first round of alignment between the two classification systems resulted in 555
possible worlds—meaning that we have 555 different ways for reconciling these two
classifications (see Figure 3 for a few examples). The alignment resulted in so many
solutions because the articulations for the Fabaceae family (the beans family) and the
Sapindaceae family (the maple family) were left ambiguous and underspecified.
    In the Cronquist system, the three families placed under the order Fabales are:
         Caesalpiniaceae sec. Cronquist
         Mimosaceae sec. Cronquist
         Fabaceae sec. Cronquist

While in the APG IV system, the order Fabales only consists of one family Fabaceae,
and under the Fabaceae there are three sub-families:
         Caesalpinioideae sec. APG IV
         Mimosoideae sec. APG IV
         Faboideae sec. APG IV

   First, the family/subfamily names between the two systems are not exactly the same,
the spelling is different in the suffix ( -ceae vs. -deae); furthermore, the ‘umbrella’ fam-
ily Fabaceae in the APG system is spelled the same as one of the three bean families in
the Cronquist system (also Fabaceae). Similarly, we raise doubts on whether the Sap-
indaceae in the Cronquist system is entirely equivalent to the Sapindaceae sec. APG
IV; though they share the exact same name, the Aceraceae sec. Cronquist, and Hippo-
castanaceae sec. Cronquist, also in the order of Sapindales, were totally void in the APG
system. Therefore, in our initial attempt we could not firmly state what the articulations
among these families were, echoing the claim that “names are not enough” in [11].
                                                                                                                                                                                                                                                                                                                                                                           7

  PW1                                 APG.Poaceae
                                       APG.Poales
                                     C.Commelinidae
                                       C.Cyperales         C.Liliales
                                                                                APG.Liliaceae
                                                                                 APG.Liliales
                                                                                 C.Liliaceae
                                                                                                                                                                                                         PW2                     APG.Poaceae
                                                                                                                                                                                                                                  APG.Poales
                                                                                                                                                                                                                                C.Commelinidae
                                                                                                                                                                                                                                  C.Cyperales
                                                                                                                                                                                                                                  C.Poaceae
                                                                                                                                                                                                                                                      C.Liliales
                                                                                                                                                                                                                                                                         APG.Liliaceae
                                                                                                                                                                                                                                                                          APG.Liliales
                                                                                                                                                                                                                                                                          C.Liliaceae

                                                                                                                                                                                                                                                                          C.Iridaceae
                                       C.Poaceae                                 C.Iridaceae                                                                                                                                                                             APG.Iridaceae
                                                                                APG.Iridaceae
                                                                                                                                                                                                                                                  APG.Asparagales
                                                       APG.Asparagales                                                                                                                                                             C.Liliidae
                                        C.Liliidae                                                                                                                                                                                                                      APG.Orchidaceae
                                                                              APG.Orchidaceae                                                                                                                                                                            C.Orchidaceae
                                                                               C.Orchidaceae                                                                                                                    C.Liliopsida
                     C.Liliopsida                                                                                                                                                                              APG.Monocots                       APG.Alismatales         C.Orchidales         APG.Solanaceae
                    APG.Monocots                        APG.Alismatales         C.Orchidales           APG.Solanaceae
                                                                                                                                                                                                                                  C.Arecidae       APG.Araceae                                  APG.Solanales
                                       C.Arecidae        APG.Araceae                                    APG.Solanales                                                                                                                               C.Araceae                                   C.Solanaceae
                                                          C.Araceae                                     C.Solanaceae                                                                                                                                 C.Arales                                    C.Solanales          APG.Lamiaceae
                                                           C.Arales                                      C.Solanales           APG.Lamiaceae                                                                                                                           APG.Papaveraceae                                C.Lamiaceae                                          Nodes
                                                                             APG.Papaveraceae                                   C.Lamiaceae                                              Nodes                                                                          C.Papaveraceae                                  C.Lamiales
                                                                              C.Papaveraceae                                     C.Lamiales                                                                                                        APG.Arecaceae         C.Papaverales                                                          C.Oleaceae              congruent         37
                                                        APG.Arecaceae                                                                                                                                                                                                                           APG.Lamiales
                                                                               C.Papaverales            APG.Lamiales                                      C.Oleaceae               congruent            37                                          APG.Arecales                                                                               APG.Oleaceae
                                                         APG.Arecales                                                                                    APG.Oleaceae                                                                               C.Arecaceae                                                                                                                C          20
                                                         C.Arecaceae                                                                                                                     C              20                                           C.Arecales       APG.Ranunculaceae                               C.Scrophulariales
                                                          C.Arecales         APG.Ranunculaceae                                 C.Scrophulariales                                                                                                                                               APG.Asteraceae                                                              APG            14
                                                                                                       APG.Asteraceae                                                                 APG               14                                                             C.Ranunculaceae                                                       C.Scrophulariaceae
                                                                              C.Ranunculaceae                                                          C.Scrophulariaceae                                                                                               C.Ranunculales          APG.Asterales                               APG.Scrophulariaceae
                                                                               C.Ranunculales           APG.Asterales                                 APG.Scrophulariaceae                                                                       APG.Magnoliaceae                               C.Asteraceae                                                                Edges
                                                       APG.Magnoliaceae                                 C.Asteraceae                                                                     Edges
                                                                                                                                                                                                                                                  APG.Magnoliales                                C.Asterales
                                                        APG.Magnoliales                                  C.Asterales                                                                                                                              APG.Magnoliids                                                                                                      is_a (inferred)     18
                                                        APG.Magnoliids                                                                                                           is_a (inferred)        18                                                                 C.Asteridae
                                                                                 C.Asteridae                                                                                                                                                      C.Magnoliaceae
                                                        C.Magnoliaceae                                                                                                                                                                                                                        APG.Caprifoliaceae                                                    overlaps (inferred) 23
                                                                                                                                                                               overlaps C.Magnoliophyta
                                                                                                                                                                                        (inferred) 24                                              C.Magnoliales
 C.Magnoliophyta                                         C.Magnoliales                                APG.Caprifoliaceae                                                                                      C.Magnoliopsida    C.Magnoliidae                                                 APG.Dipsacales
                   C.Magnoliopsida    C.Magnoliidae                                                    APG.Dipsacales                                                                  APG.Angiosperms                                                                                                                                                                  is_a (input)      68
APG.Angiosperms                                                                                                                                                                   is_a (input)     68                                                                    APG.Ericaceae         C.Caprifoliaceae
                                                                                APG.Ericaceae          C.Caprifoliaceae                                                                                                                          APG.BasalEudicots        APG.Ericales          C.Dipsacales
                                                      APG.BasalEudicots          APG.Ericales           C.Dipsacales                                                                                                                             APG.Ranunculales         C.Ericaceae
                                                      APG.Ranunculales           C.Ericaceae                                                                                                                                                                               C.Ericales
                                                                                  C.Ericales                                                                                                                                                                                                 APG.Asclepiadaceae
                                                                                                     APG.Asclepiadaceae                                                                                                                                                                       APG.Gentianales
                                                                                                      APG.Gentianales                                                                                                                                                    APG.Apiaceae         C.Asclepiadaceae       C.Caryophyllaceae
                                                                                APG.Apiaceae          C.Asclepiadaceae        C.Caryophyllaceae                                                                                                   APG.AsteridClade        APG.Apiales           C.Gentianales       APG.Caryophyllaceae
                                                       APG.AsteridClade          APG.Apiales            C.Gentianales        APG.Caryophyllaceae                                                                                                                          C.Apiaceae
                                                                                 C.Apiaceae                                                                                                                                                                                C.Apiales
                                                                                  C.Apiales                                                                                                                                                                                                                           C.Portulacaceae
                                                                                                                               C.Portulacaceae                                                                                                                                                 C.Caryophyllales
                                                                                                       C.Caryophyllales                                                                                                                                                                                              APG.Portulacaceae
                                                                                                                              APG.Portulacaceae                                                                                                                       APG.Caryophyllales
                                                                             APG.Caryophyllales                                                                                                                                                                      APG.CaryophyllidClade
                                                                            APG.CaryophyllidClade                                                                                                                                                                                             APG.Polygonaceae         C.Cactaceae
                                                                                                      APG.Polygonaceae          C.Cactaceae                                                                                                                                                    C.Polygonaceae         APG.Cactaceae
                                                                                                       C.Polygonaceae          APG.Cactaceae                                                                                                                                                    C.Polygonales
                                                                                                        C.Polygonales                                                                                                                                                      C.Violales
                                                                                  C.Violales
                                                                                                                                                                                                                                 APG.Eudicots     C.Caryophyllidae
                                      APG.Eudicots      C.Caryophyllidae                                                                                                                                                                                                                      APG.Cucurbitaceae
                                                                                                      APG.Cucurbitaceae                                                                                                                                                                        APG.Cucurbitales
                                                                                                       APG.Cucurbitales                                                                                                                                                                        C.Cucurbitaceae
                                                                                                       C.Cucurbitaceae
                                                                                                                                                                                                                                                                        APG.Malvaceae
                                                                               APG.Malvaceae                                                                                                                                                                             APG.Malvales            C.Violaceae
                                                                                APG.Malvales             C.Violaceae                                                                                                                                                     C.Malvaceae            APG.Violaceae
                                                                                C.Malvaceae             APG.Violaceae                                                                                                                                                     C.Malvales
                                                                                 C.Malvales
                                                                                                                                                                                                                                                                                               APG.Salicaceae
                                                                                                       APG.Salicaceae                                                                                                                                                  APG.Brassicaceae         C.Salicaceae
                                                                              APG.Brassicaceae          C.Salicaceae                                                                                                                                                    APG.Brassicales
                                                                               APG.Brassicales                                                                                                                                                                                                   C.Salicales
                                                                                                         C.Salicales                                                                                                                                                    C.Brassicaceae
                                                                               C.Brassicaceae                                                                                                                                                                            C.Capparales                                C.Caesalpiniaceae
                                                                                C.Capparales                                    C.Mimosaceae

                                                                                                                                                                                                                                                                        APG.Malpighiales         C.Fabaceae          APG.Mimosoideae
                                                                              APG.Malpighiales           C.Fabaceae           C.Caesalpiniaceae
                                                                                                                                                                                                                                                  APG.RosidClade
                                                        APG.RosidClade
                                                                                                                                                                                                                                                                           C.Fabales            APG.Fabaceae
                                                                                  C.Fabales             APG.Fabaceae                                                                                                                                                                                                   APG.Faboideae
                                                                                                                              APG.Mimosoideae                                                                                                                                                    APG.Fabales
                                                                                                         APG.Fabales
                                                                                                                                                                                                                                                                         APG.Myrtales
                                                                               APG.Myrtales                                                                                                                                                                             APG.Onagraceae                              APG.Caesalpinioideae
                                                                              APG.Onagraceae                                    APG.Faboideae                                                                                                        C.Rosidae                                APG.Euphorbiaceae
                                                           C.Rosidae                                 APG.Euphorbiaceae                                                                                                                                                     C.Myrtales
                                                                                 C.Myrtales                                                                                                                                                                              C.Onagraceae          C.Euphorbiaceae
                                                                               C.Onagraceae           C.Euphorbiaceae                                                                                                                                                                           C.Euphorbiales
                                                                                                       C.Euphorbiales                                                                                                                                                                                                  C.Mimosaceae
                                                                                                                             APG.Caesalpinioideae

                                                                                                                                                                                                                                                                                                APG.Rosaceae
                                                                                                        APG.Rosaceae                                                                                                                                                                             C.Rosaceae
                                                                                                         C.Rosaceae                                                                                                                                                                                                 C.Hippocastanaceae
                                                                                                                             C.Hippocastanaceae                                                                                                                                                   C.Rosales
                                                                                                          C.Rosales
                                                                                                                                                                                                                                                                          APG.Rosales
                                                                                APG.Rosales                                                                                                                                                                                                      C.Sapindales           C.Aceraceae
                                                                                                        C.Sapindales             C.Aceraceae
                                                                                                                                                                                                                                                                       APG.Sapindaceae
                                                                              APG.Sapindaceae                                                                                                                                                                           APG.Sapindales           C.Fagaceae
                                                                               APG.Sapindales            C.Fagaceae                                                                                                                                                                             APG.Fagaceae           C.Sapindaceae
                                                                                                        APG.Fagaceae            C.Sapindaceae
                                                                                                                                                                                                                                                                           C.Fagales
                                                                                 C.Fagales                                                                                                                                                                                APG.Fagales           C.Betulaceae
                                                                                APG.Fagales             C.Betulaceae                                                                                                                                                                           APG.Betulaceae
                                                                                                                                                                                                                                                   C.Hamamelidae
                                                        C.Hamamelidae                                  APG.Betulaceae

                                                                                                                                                                                                                                                                                                APG.Moraceae
                                                                                                        APG.Moraceae                                                                                                                                                                             C.Moraceae
                                                                                                         C.Moraceae                                                                                                                                                    APG.CoreEudicots          C.Urticales
                                                                             APG.CoreEudicots            C.Urticales                                                                                                                                                  APG.Hamamelidaceae
                                                                            APG.Hamamelidaceae                                                                                                                                                                          APG.Saxifragales
                                                                              APG.Saxifragales                                                                                                                                                                         C.Hamamelidaceae
                                                                             C.Hamamelidaceae                                                                                                                                                                           C.Hamamelidales
                                                                              C.Hamamelidales




                                                                                                                                                                                                                                                                         APG.Liliaceae
                                                                                                                                                                                                                                 APG.Poaceae                              APG.Liliales
                                                                               APG.Liliaceae                                                                                                                                      APG.Poales                              C.Liliaceae



    PW3                                                                                                                                                                                                  PW4
                                      APG.Poaceae                               APG.Liliales                                                                                                                                    C.Commelinidae
                                       APG.Poales                               C.Liliaceae                                                                                                                                       C.Cyperales         C.Liliales
                                     C.Commelinidae                                                                                                                                                                               C.Poaceae                               C.Iridaceae
                                       C.Cyperales        C.Liliales                                                                                                                                                                                                     APG.Iridaceae
                                       C.Poaceae                               C.Iridaceae
                                                                              APG.Iridaceae                                                                                                                                                       APG.Asparagales
                                                                                                                                                                                                                                   C.Liliidae
                                                                                                                                                                                                                                                                        APG.Orchidaceae
                                        C.Liliidae    APG.Asparagales                                                                                                                                                                                                    C.Orchidaceae
                                                                             APG.Orchidaceae                                                                                                                   C.Liliopsida
                                                                                                                                                                                                              APG.Monocots                        APG.Alismatales         C.Orchidales         APG.Solanaceae
                    C.Liliopsida                                              C.Orchidaceae                                                                                                                                                        APG.Araceae                                  APG.Solanales
                   APG.Monocots                        APG.Alismatales         C.Orchidales          APG.Solanaceae                                                                                                               C.Arecidae
                                                                                                                                                                                                                                                    C.Araceae                                   C.Solanaceae
                                                        APG.Araceae                                   APG.Solanales                                                                                                                                  C.Arales                                    C.Solanales           APG.Lamiaceae
                                       C.Arecidae        C.Araceae                                    C.Solanaceae                                                                                                                                                     APG.Papaveraceae                                 C.Lamiaceae                                            Nodes
                                                          C.Arales                                     C.Solanales           APG.Lamiaceae                                                                                                                              C.Papaveraceae                                   C.Lamiales
                                                                            APG.Papaveraceae                                  C.Lamiaceae                                           Nodes                                                         APG.Arecaceae          C.Papaverales           APG.Lamiales                                    C.Oleaceae              congruent            37
                                                                             C.Papaveraceae                                    C.Lamiales                                                                                                          APG.Arecales                                                                                 APG.Oleaceae
                                                       APG.Arecaceae          C.Papaverales                                                             C.Oleaceae              congruent          37                                              C.Arecaceae                                                                                                                 C              20
                                                        APG.Arecales                                  APG.Lamiales
                                                                                                                                                       APG.Oleaceae                                                                                 C.Arecales        APG.Ranunculaceae                               C.Scrophulariales
                                                        C.Arecaceae                                                                                                                  C             20                                                                                           APG.Asteraceae                                                              APG               14
                                                         C.Arecales                                                          C.Scrophulariales                                                                                                                         C.Ranunculaceae                                                       C.Scrophulariaceae
                                                                            APG.Ranunculaceae                                                                                                                                                                           C.Ranunculales           APG.Asterales                              APG.Scrophulariaceae
                                                                             C.Ranunculaceae         APG.Asteraceae                                  C.Scrophulariaceae            APG             14                                            APG.Magnoliaceae                                C.Asteraceae                                                                  Edges
                                                                              C.Ranunculales          APG.Asterales                                 APG.Scrophulariaceae
                                                      APG.Magnoliaceae                                C.Asteraceae                                                                  Edges                                                         APG.Magnoliales                                 C.Asterales
                                                                                                                                                                                                                                                  APG.Magnoliids                                                                                                       is_a (inferred)        18
                                                       APG.Magnoliales                                 C.Asterales                                                                                                                                C.Magnoliaceae           C.Asteridae
                                                       APG.Magnoliids                                                                                                          is_a (inferred)   18                                                                                                                                                                  overlaps (inferred) 22
                                                                                C.Asteridae                                                                                              C.Magnoliophyta                                           C.Magnoliales                              APG.Caprifoliaceae
                                                       C.Magnoliaceae                                                                                                                                         C.Magnoliopsida    C.Magnoliidae                                                 APG.Dipsacales
                                                        C.Magnoliales                               APG.Caprifoliaceae                                                       overlaps (inferred) 23
                                                                                                                                                                                        APG.Angiosperms                                                                                                                                                                  is_a (input)         68
 C.Magnoliophyta   C.Magnoliopsida   C.Magnoliidae                                                                                                                                                                                                                       APG.Ericaceae         C.Caprifoliaceae
APG.Angiosperms                                                                                      APG.Dipsacales                                                             is_a (input)       68
                                                                                                     C.Caprifoliaceae                                                                                                                            APG.BasalEudicots        APG.Ericales          C.Dipsacales
                                                                              APG.Ericaceae                                                                                                                                                      APG.Ranunculales
                                                      APG.BasalEudicots        APG.Ericales           C.Dipsacales                                                                                                                                                        C.Ericaceae
                                                      APG.Ranunculales         C.Ericaceae                                                                                                                                                                                 C.Ericales
                                                                                                                                                                                                                                                                                              APG.Asclepiadaceae
                                                                                C.Ericales                                                                                                                                                                                                     APG.Gentianales
                                                                                                    APG.Asclepiadaceae
                                                                                                     APG.Gentianales                                                                                                                                                     APG.Apiaceae          C.Asclepiadaceae      C.Caryophyllaceae
                                                                                                     C.Asclepiadaceae       C.Caryophyllaceae                                                                                                    APG.AsteridClade         APG.Apiales            C.Gentianales      APG.Caryophyllaceae
                                                                              APG.Apiaceae
                                                      APG.AsteridClade         APG.Apiales             C.Gentianales       APG.Caryophyllaceae                                                                                                                            C.Apiaceae
                                                                               C.Apiaceae                                                                                                                                                                                  C.Apiales
                                                                                                                                                                                                                                                                                                                      C.Portulacaceae
                                                                                C.Apiales                                                                                                                                                                                                      C.Caryophyllales
                                                                                                                             C.Portulacaceae                                                                                                                                                                         APG.Portulacaceae
                                                                                                     C.Caryophyllales                                                                                                                                                 APG.Caryophyllales
                                                                                                                            APG.Portulacaceae
                                                                            APG.Caryophyllales                                                                                                                                                                       APG.CaryophyllidClade
                                                                           APG.CaryophyllidClade
                                                                                                                                                                                                                                                                                              APG.Polygonaceae          C.Cactaceae
                                                                                                    APG.Polygonaceae          C.Cactaceae                                                                                                                                                      C.Polygonaceae          APG.Cactaceae
                                                                                                     C.Polygonaceae          APG.Cactaceae                                                                                                                                                      C.Polygonales
                                                                                                                                                                                                                                                                           C.Violales
                                                                                                      C.Polygonales
                                                                                 C.Violales
                                                                                                                                                                                                                                 APG.Eudicots     C.Caryophyllidae
                                                                                                                                                                                                                                                                                              APG.Cucurbitaceae
                                      APG.Eudicots     C.Caryophyllidae                                                                                                                                                                                                                        APG.Cucurbitales
                                                                                                    APG.Cucurbitaceae
                                                                                                     APG.Cucurbitales                                                                                                                                                                          C.Cucurbitaceae
                                                                                                     C.Cucurbitaceae
                                                                                                                                                                                                                                                                         APG.Malvaceae
                                                                              APG.Malvaceae                                                                                                                                                                               APG.Malvales           C.Violaceae
                                                                               APG.Malvales            C.Violaceae                                                                                                                                                        C.Malvaceae           APG.Violaceae
                                                                               C.Malvaceae            APG.Violaceae                                                                                                                                                        C.Malvales
                                                                                C.Malvales
                                                                                                                                                                                                                                                                                                APG.Salicaceae
                                                                                                      APG.Salicaceae                                                                                                                                                   APG.Brassicaceae          C.Salicaceae
                                                                             APG.Brassicaceae          C.Salicaceae                                                                                                                                                     APG.Brassicales
                                                                              APG.Brassicales                                                                                                                                                                                                     C.Salicales
                                                                                                        C.Salicales                                                                                                                                                     C.Brassicaceae
                                                                              C.Brassicaceae                                                                                                                                                                             C.Capparales                                 APG.Mimosoideae
                                                                               C.Capparales                                 C.Caesalpiniaceae

                                                                                                                                                                                                                                                                        APG.Malpighiales         C.Fabaceae            APG.Faboideae
                                                                             APG.Malpighiales          C.Fabaceae            APG.Faboideae
                                                                                                                                                                                                                                                  APG.RosidClade
                                                       APG.RosidClade
                                                                                                                                                                                                                                                                           C.Fabales            APG.Fabaceae        APG.Caesalpinioideae
                                                                                C.Fabales             APG.Fabaceae                                                                                                                                                                               APG.Fabales
                                                                                                       APG.Fabales          APG.Mimosoideae

                                                                                                                                                                                                                                                                         APG.Myrtales
                                                                              APG.Myrtales                                                                                                                                                                              APG.Onagraceae                                 C.Mimosaceae
                                                                             APG.Onagraceae                                APG.Caesalpinioideae                                                                                                      C.Rosidae                                APG.Euphorbiaceae
                                                          C.Rosidae                                 APG.Euphorbiaceae                                                                                                                                                      C.Myrtales
                                                                                C.Myrtales                                                                                                                                                                               C.Onagraceae          C.Euphorbiaceae
                                                                              C.Onagraceae           C.Euphorbiaceae                                                                                                                                                                            C.Euphorbiales
                                                                                                      C.Euphorbiales
                                                                                                                                                                                                                                                                                                                      C.Caesalpiniaceae
                                                                                                                              C.Mimosaceae

                                                                                                      APG.Rosaceae
                                                                                                                                                                                                                                                                                                APG.Rosaceae
                                                                                                       C.Rosaceae                                                                                                                                                                                C.Rosaceae
                                                                                                                           C.Hippocastanaceae                                                                                                                                                                        C.Hippocastanaceae
                                                                                                        C.Rosales                                                                                                                                                                                 C.Rosales

                                                                               APG.Rosales                                                                                                                                                                                APG.Rosales
                                                                                                       C.Sapindales            C.Aceraceae                                                                                                                                                       C.Sapindales           C.Aceraceae

                                                                             APG.Sapindaceae                                                                                                                                                                            APG.Sapindaceae
                                                                              APG.Sapindales           C.Fagaceae                                                                                                                                                        APG.Sapindales          C.Fagaceae
                                                                                                                              C.Sapindaceae                                                                                                                                                     APG.Fagaceae           C.Sapindaceae
                                                                                                      APG.Fagaceae
                                                                                C.Fagales                                                                                                                                                                                  C.Fagales
                                                                               APG.Fagales            C.Betulaceae                                                                                                                                                        APG.Fagales            C.Betulaceae
                                                       C.Hamamelidae                                 APG.Betulaceae                                                                                                                               C.Hamamelidae                                 APG.Betulaceae


                                                                                                      APG.Moraceae                                                                                                                                                                              APG.Moraceae
                                                                                                       C.Moraceae                                                                                                                                                                                C.Moraceae
                                                                            APG.CoreEudicots           C.Urticales
                                                                                                                                                                                                                                                                       APG.CoreEudicots          C.Urticales
                                                                           APG.Hamamelidaceae                                                                                                                                                                         APG.Hamamelidaceae
                                                                             APG.Saxifragales                                                                                                                                                                           APG.Saxifragales
                                                                            C.Hamamelidaceae                                                                                                                                                                           C.Hamamelidaceae
                                                                             C.Hamamelidales                                                                                                                                                                            C.Hamamelidales




                                                                                APG.Liliaceae                                                                                                                                                                            APG.Liliaceae
                                      APG.Poaceae                                APG.Liliales                                                                                                                                    APG.Poaceae



                                                                                                                                                                                                             PW6
                                                                                                                                                                                                                                                                          APG.Liliales




            PW5
                                       APG.Poales                                C.Liliaceae                                                                                                                                      APG.Poales
                                     C.Commelinidae                                                                                                                                                                                                                       C.Liliaceae
                                                                                                                                                                                                                                C.Commelinidae
                                       C.Cyperales         C.Liliales                                                                                                                                                             C.Cyperales        C.Liliales
                                       C.Poaceae                                 C.Iridaceae                                                                                                                                      C.Poaceae                              C.Iridaceae
                                                                                APG.Iridaceae                                                                                                                                                                           APG.Iridaceae
                                                       APG.Asparagales                                                                                                                                                                           APG.Asparagales
                                        C.Liliidae                                                                                                                                                                                 C.Liliidae
                                                                              APG.Orchidaceae                                                                                                                                                                          APG.Orchidaceae
                     C.Liliopsida                                              C.Orchidaceae                                                                                                                                                                            C.Orchidaceae
                                                                                C.Orchidales                                                                                                                   C.Liliopsida
                    APG.Monocots                        APG.Alismatales                                APG.Solanaceae                                                                                         APG.Monocots                        APG.Alismatales        C.Orchidales         APG.Solanaceae
                                                         APG.Araceae                                    APG.Solanales                                                                                                                              APG.Araceae                                 APG.Solanales
                                       C.Arecidae                                                                                                                                                                                 C.Arecidae
                                                          C.Araceae                                     C.Solanaceae                                                                                                                                C.Araceae                                  C.Solanaceae
                                                           C.Arales                                      C.Solanales           APG.Lamiaceae                                                                                                         C.Arales                                   C.Solanales          APG.Lamiaceae
                                                                             APG.Papaveraceae                                   C.Lamiaceae                                              Nodes                                                                        APG.Papaveraceae                                C.Lamiaceae                                         Nodes
                                                                              C.Papaveraceae                                     C.Lamiales                                                                                                                            C.Papaveraceae                                  C.Lamiales
                                                        APG.Arecaceae          C.Papaverales                                                              C.Oleaceae               congruent            37                                        APG.Arecaceae
                                                                                                        APG.Lamiales                                                                                                                                                    C.Papaverales          APG.Lamiales                                    C.Oleaceae              congruent         37
                                                         APG.Arecales                                                                                    APG.Oleaceae                                                                              APG.Arecales
                                                         C.Arecaceae                                                                                                                                                                                                                                                                          APG.Oleaceae
                                                                                                                                                                                         C              20                                         C.Arecaceae                                                                                                             C             20
                                                          C.Arecales         APG.Ranunculaceae                                 C.Scrophulariales                                                                                                                                                                     C.Scrophulariales
                                                                                                                                                                                                                                                    C.Arecales        APG.Ranunculaceae
                                                                              C.Ranunculaceae          APG.Asteraceae                                  C.Scrophulariaceae             APG               14                                                                                    APG.Asteraceae                                                             APG             14
                                                                                                        APG.Asterales                                                                                                                                                  C.Ranunculaceae                                                      C.Scrophulariaceae
                                                                               C.Ranunculales                                                         APG.Scrophulariaceae               Edges                                                                          C.Ranunculales         APG.Asterales                               APG.Scrophulariaceae
                                                       APG.Magnoliaceae                                 C.Asteraceae                                                                                                                             APG.Magnoliaceae                              C.Asteraceae                                                               Edges
                                                        APG.Magnoliales                                  C.Asterales                                                                                                                              APG.Magnoliales                               C.Asterales
                                                        APG.Magnoliids                                                                                                           is_a (inferred)        18                                                                                                                                                           is_a (inferred)     18
                                                                                 C.Asteridae                                                                                                                                                      APG.Magnoliids
                                                        C.Magnoliaceae                                                                                                                                                                            C.Magnoliaceae          C.Asteridae
                                                                                                      APG.Caprifoliaceae                                                       overlaps (inferred) 23                                                                                                                                                              overlaps (inferred) 22
 C.Magnoliophyta                                         C.Magnoliales                                                                                                                  C.Magnoliophyta                                            C.Magnoliales                             APG.Caprifoliaceae
APG.Angiosperms    C.Magnoliopsida    C.Magnoliidae                                                    APG.Dipsacales                                                                                         C.Magnoliopsida   C.Magnoliidae
                                                                                                                                                                                  is_a APG.Angiosperms
                                                                                                                                                                                       (input)     68                                                                                         APG.Dipsacales                                                          is_a (input)       68
                                                                                APG.Ericaceae          C.Caprifoliaceae                                                                                                                                                 APG.Ericaceae         C.Caprifoliaceae
                                                      APG.BasalEudicots          APG.Ericales           C.Dipsacales                                                                                                                             APG.BasalEudicots       APG.Ericales          C.Dipsacales
                                                      APG.Ranunculales           C.Ericaceae                                                                                                                                                     APG.Ranunculales        C.Ericaceae
                                                                                  C.Ericales                                                                                                                                                                              C.Ericales
                                                                                                     APG.Asclepiadaceae                                                                                                                                                                      APG.Asclepiadaceae
                                                                                                      APG.Gentianales                                                                                                                                                                         APG.Gentianales
                                                                                APG.Apiaceae          C.Asclepiadaceae        C.Caryophyllaceae                                                                                                                         APG.Apiaceae          C.Asclepiadaceae      C.Caryophyllaceae
                                                       APG.AsteridClade          APG.Apiales            C.Gentianales        APG.Caryophyllaceae                                                                                                 APG.AsteridClade        APG.Apiales            C.Gentianales      APG.Caryophyllaceae
                                                                                 C.Apiaceae                                                                                                                                                                              C.Apiaceae
                                                                                  C.Apiales                                                                                                                                                                               C.Apiales
                                                                                                                               C.Portulacaceae                                                                                                                                                                       C.Portulacaceae
                                                                                                       C.Caryophyllales       APG.Portulacaceae                                                                                                                                               C.Caryophyllales      APG.Portulacaceae
                                                                             APG.Caryophyllales                                                                                                                                                                       APG.Caryophyllales
                                                                            APG.CaryophyllidClade                                                                                                                                                                    APG.CaryophyllidClade
                                                                                                      APG.Polygonaceae          C.Cactaceae                                                                                                                                                  APG.Polygonaceae         C.Cactaceae
                                                                                                       C.Polygonaceae          APG.Cactaceae                                                                                                                                                  C.Polygonaceae         APG.Cactaceae
                                                                                                        C.Polygonales                                                                                                                                                                          C.Polygonales
                                                                                  C.Violales                                                                                                                                                                               C.Violales
                                      APG.Eudicots      C.Caryophyllidae                                                                                                                                                         APG.Eudicots     C.Caryophyllidae
                                                                                                      APG.Cucurbitaceae                                                                                                                                                                      APG.Cucurbitaceae
                                                                                                       APG.Cucurbitales                                                                                                                                                                       APG.Cucurbitales
                                                                                                       C.Cucurbitaceae                                                                                                                                                                        C.Cucurbitaceae
                                                                               APG.Malvaceae                                                                                                                                                                            APG.Malvaceae
                                                                                APG.Malvales             C.Violaceae                                                                                                                                                     APG.Malvales           C.Violaceae
                                                                                C.Malvaceae             APG.Violaceae                                                                                                                                                    C.Malvaceae           APG.Violaceae
                                                                                 C.Malvales                                                                                                                                                                               C.Malvales

                                                                                                       APG.Salicaceae                                                                                                                                                                          APG.Salicaceae
                                                                              APG.Brassicaceae          C.Salicaceae                                                                                                                                                   APG.Brassicaceae
                                                                               APG.Brassicales                                                                                                                                                                                                  C.Salicaceae
                                                                                                         C.Salicales                                                                                                                                                    APG.Brassicales          C.Salicales
                                                                               C.Brassicaceae                                                                                                                                                                           C.Brassicaceae
                                                                                C.Capparales                                    C.Mimosaceae                                                                                                                             C.Capparales                               C.Caesalpiniaceae


                                                                              APG.Malpighiales           C.Fabaceae           C.Caesalpiniaceae                                                                                                                        APG.Malpighiales         C.Fabaceae          APG.Mimosoideae
                                                        APG.RosidClade                                                                                                                                                                            APG.RosidClade
                                                                                  C.Fabales             APG.Fabaceae                                                                                                                                                      C.Fabales            APG.Fabaceae
                                                                                                         APG.Fabales          APG.Mimosoideae                                                                                                                                                                        APG.Faboideae
                                                                                                                                                                                                                                                                                                APG.Fabales

                                                                               APG.Myrtales                                                                                                                                                                             APG.Myrtales
                                                                              APG.Onagraceae                                    APG.Faboideae                                                                                                                          APG.Onagraceae                              APG.Caesalpinioideae
                                                           C.Rosidae                                 APG.Euphorbiaceae                                                                                                                               C.Rosidae                               APG.Euphorbiaceae
                                                                                 C.Myrtales                                                                                                                                                                               C.Myrtales
                                                                               C.Onagraceae           C.Euphorbiaceae                                                                                                                                                   C.Onagraceae          C.Euphorbiaceae
                                                                                                       C.Euphorbiales                                                                                                                                                                          C.Euphorbiales
                                                                                                                             APG.Caesalpinioideae                                                                                                                                                                     C.Mimosaceae

                                                                                                        APG.Rosaceae                                                                                                                                                                           APG.Rosaceae
                                                                                                         C.Rosaceae          C.Hippocastanaceae                                                                                                                                                 C.Rosaceae
                                                                                                          C.Rosales                                                                                                                                                                              C.Rosales         C.Hippocastanaceae

                                                                                APG.Rosales                                                                                                                                                                              APG.Rosales
                                                                                                        C.Sapindales             C.Aceraceae                                                                                                                                                    C.Sapindales           C.Aceraceae

                                                                              APG.Sapindaceae                                                                                                                                                                          APG.Sapindaceae
                                                                               APG.Sapindales            C.Fagaceae                                                                                                                                                     APG.Sapindales          C.Fagaceae
                                                                                                        APG.Fagaceae            C.Sapindaceae                                                                                                                                                                         C.Sapindaceae
                                                                                                                                                                                                                                                                                               APG.Fagaceae
                                                                                 C.Fagales                                                                                                                                                                                C.Fagales
                                                                                APG.Fagales             C.Betulaceae                                                                                                                                                     APG.Fagales           C.Betulaceae
                                                        C.Hamamelidae                                  APG.Betulaceae                                                                                                                             C.Hamamelidae                               APG.Betulaceae

                                                                                                        APG.Moraceae                                                                                                                                                                           APG.Moraceae
                                                                                                         C.Moraceae                                                                                                                                                                             C.Moraceae
                                                                             APG.CoreEudicots            C.Urticales                                                                                                                                                  APG.CoreEudicots          C.Urticales
                                                                            APG.Hamamelidaceae                                                                                                                                                                       APG.Hamamelidaceae
                                                                              APG.Saxifragales                                                                                                                                                                         APG.Saxifragales
                                                                             C.Hamamelidaceae                                                                                                                                                                         C.Hamamelidaceae
                                                                              C.Hamamelidales                                                                                                                                                                          C.Hamamelidales




Fig. 3. Six of the 555 possible worlds to model the merged view of the two classification, with
                         the main differences marked in the red boxes.
                                                                                                                                                                                                       APG.Lamiales
                                                                                                                                                    =            APG.Oleaceae
                                                                                       C.Scrophulariales                    C.Oleaceae


                                                                                                                         C.Asclepiadaceae           =
                                                                                        C.Gentianales                                                         APG.Asclepiadaceae
                                                                                                                                                                                                      APG.Gentianales

                                                      C.Asteridae                        C.Dipsacales                     C.Caprifoliaceae          =
                                                                                                                                                               APG.Caprifoliaceae
                                                                                                                                                                                                      APG.Dipsacales

                                                                                         C.Solanales                       C.Solanaceae             =
                                                                                                                                                                APG.Solanaceae                         APG.Solanales
                                                                                                                                                                                                                           A
                                                                                         C.Asterales                                                =                                                  APG.Asterales
                                                                                                                           C.Asteraceae                         APG.Asteraceae


                                                                                                                                 =                                                   APG.Apiales
                                                                                                                                               APG.Apiaceae
                                                                                                           C.Apiaceae
                                                                                                                                                                                                        APG.Ericales
                                                                       C.Apiales                                                                    =           APG.Ericaceae
                                                                                                                            C.Ericaceae

                                                                                                                                                                                                                          APG
                                           8                                              C.Ericales                        C.Cactaceae             =           APG.Cactaceae


                                                                                                                         C.Caryophyllaceae          =         APG.Caryophyllaceae                    APG.Caryophyllales


                                               After consulting the domain expert on our secondC.Portulacaceae
                                                                                                           round of alignment, we APG.Portulacaceae
                                                                                                                                     were able
                                                                                       C.Caryophyllales
                                                                                                                                                    =

                                           to refine our alignments between       the two taxonomies C.Polygonaceae
                                                                             C.Polygonales                and make the relationships
                                                                                                                             =
                                                                                                                                          among
                                                                                                                                     APG.Polygonaceae

C.Magnoliophyta   C.Magnoliopsida
                                           the beans    families explicit. Despite
                                                   C.Caryophyllidae
                                                                                       the slight differences in the suffix, the three families
                                                                               C.Salicales
                                           under Cronquist indeed were congruent
                                                                               C.Violales
                                                                                             to the three sub-families
                                                                                                           C.Salicaceae
                                                                                                                          within
                                                                                                                             =
                                                                                                                                 the APG       sys-
                                                                                                                                      APG.Salicaceae
                                           tem (Figure 4), and that the Sapindaceae sec. Cronquist,              Aceraceae sec.
                                                                                                            C.Violaceae      =  Cronquist, and
                                           Hippocastanaceae sec. Cronquist are all combined as one as Sapindaceae sec. APG IV
                                                                              C.Capparales                                             APG.Violaceae

                                                                                                          C.Cucurbitaceae    =                                                                        APG.Malpighiales
                                           now.                                C.Malvales
                                                                                                                                     APG.Cucurbitaceae
                                                                                                                           C.Brassicaceae           =                                                 APG.Cucurbitales
                                                                     C.Euphorbiales                                                                            APG.Brassicaceae

                                                                                                                          C.Euphorbiaceae           =
                                                                                                                                                              APG.Euphorbiaceae
                                                                                        C.Mimosaceae                                                                                                  APG.Brassicales
                                                                                                               =
                                                                                                                            C.Malvaceae             =
                                    C.Rosidae          C.Fabales                         C.Fabaceae                                                             APG.Malvaceae                          APG.Malvales
                                                                                                               =         APG.Mimosoideae

                                                                                      C.Caesalpiniaceae                                                                                                 APG.Fabales
                                                                                                               =          APG.Faboideae                         APG.Fabaceae

                                                                                      C.Hippocastanaceae       <        APG.Caesalpinioideae                                        APG.Sapindales
                                                      C.Sapindales
                                                                                                               <
                                                                                         C.Aceraceae                     APG.Sapindaceae
                                                                                                               <

                                                                                        C.Sapindaceae                                                                                APG.Myrtales
                                                       C.Myrtales
                                                                                                                          APG.Onagraceae
                                                                                                               =
                                                Fig. 4. Refinement of the inputC.Onagraceae
                                                                                alignment to align the Fabaceae and the Sapinadeae
                                                                                                                         =
                                                                                                                                   family
                                                                                                                                  APG.Betulaceae                                                        APG.Fagales
                                                                                                                                                                                                                           A

                                                                                                                            C.Betulaceae

                                                                                                                                                    =           APG.Fagaceae
                                               Given this refinement in theC.Fagales
                                                                                 relationship among the          beans and the maple families,
                                                                                                            C.Fagaceae

                                           instead of having 555 possible worlds, we were able to reduce        =         theAPG.Rosaceae
                                                                                                                              ambiguities and thus                                                     APG.Rosales

                                           the number of possible     worlds to only one C.Rosaceae
                                                                C.Rosales
                                                                                               unique possible world (Figure      =
                                                                                                                                          5), where     we
                                                                                                                                              APG.Moraceae
                                           can seeC.Hamamelidae
                                                    the congruence in families,
                                                                              C.Urticales the inferred relationship among the higher-level
                                                                                                            C.Moraceae
                                                                                                                                                                                                      APG.Saxifragales

                                           nodes, and the two original classifications.
                                                                           C.Hamamelidales        All theC.Hamamelidaceae
                                                                                                          results can be retrieved=
                                                                                                                                              from our
                                                                                                                                            APG.Hamamelidaceae


                                           Github repository (https://github.com/yiyunyc2/NKOS18).              =




                                           6         Conclusion
                                           New developments, whether in technologies or in paradigms, always challenge the
                                           views of past major knowledge organization systems. In the biodiversity domain, mo-
                                           lecular data when examined under careful sampling, can provide valuable pointers to
                                           the classification of plants. However, to quote [12]: “... molecular characters are subject
                                           to evolutionary convergence, parallelism, and reversal; therefore, molecular methods
                                           are not a panacea. Molecular evidence should be used with, not in place of, morpholog-
                                           ical evidence.” Though the APG system has shown more substantial importance in re-
                                           cent years due to the advancement in micro-level analysis of the molecular data, the
                                           Cronquist system still maintains its esteemed role for its comprehensiveness and pre-
                                           ciseness in morphologically classifying the flowering plants.
                                               This paper serves as an exploratory research on the comparison and alignment of
                                           two KOS, specifically classification schemes. Our approach suggests that classifica-
                                           tions can coexist with each other while disambiguating the names among concepts in a
                                           merged possible world. Our approach also demonstrates the capability of computation-
                                           ally solving complex logic-based alignments for cases where, e.g., due to underspeci-
                                           fied relations in the input KOS alignments, manual efforts would likely fail to yield all
                                           555 different ways to merge and reconcile the two KOS.
                                                                                                                                                             9


                                                                                                        C.Fagaceae
                                                                                                       APG.Fagaceae

                                                                             APG.CoreEudicots          C.Betulaceae
                                                                            APG.Hamamelidaceae        APG.Betulaceae
                                                                              APG.Saxifragales
                                                                             C.Hamamelidaceae
                                                                              C.Hamamelidales          C.Fabaceae
                                                                                                      APG.Faboideae
                                                                                 C.Fagales
                                                                                APG.Fagales          C.Caesalpiniaceae
                                                                                                    APG.Caesalpinioideae
                                                                               APG.Fabaceae
                                                         C.Hamamelidae          APG.Fabales           C.Mimosaceae
                                                                                 C.Fabales           APG.Mimosoideae

                                                                                                       APG.Moraceae
                                                                                                        C.Moraceae
                                                                                                        C.Urticales
                                                                                APG.Rosales
                                                                                                       APG.Rosaceae
                                                                                                        C.Rosaceae
                                                                                                         C.Rosales

                                                                              APG.Sapindaceae
                                                                               APG.Sapindales       C.Hippocastanaceae
                                                                                C.Sapindales

                                                            C.Rosidae                                   C.Aceraceae

                                                                               APG.Myrtales
                                                                              APG.Onagraceae           C.Sapindaceae
                                                                                 C.Myrtales
                                                                               C.Onagraceae
                                                         APG.RosidClade
                                                                                                    APG.Euphorbiaceae
                                                                              APG.Malpighiales       C.Euphorbiaceae
                                                                                                      C.Euphorbiales

                                                                               APG.Malvaceae
                                                                                APG.Malvales            C.Violaceae
                                                                                C.Malvaceae            APG.Violaceae
                                                                                 C.Malvales

                                                                                                     APG.Cucurbitaceae
                                                                                  C.Violales          APG.Cucurbitales
                                                                                                      C.Cucurbitaceae

                                                                               APG.Apiaceae
                                                                                APG.Apiales
                                                                                C.Apiaceae
                                                                                 C.Apiales            APG.Salicaceae
                                                                                                       C.Salicaceae
                                                                                                        C.Salicales
                                                                              APG.Brassicaceae                               C.Portulacaceae
                                                                               APG.Brassicales                              APG.Portulacaceae
                                                                               C.Brassicaceae
                                                                                C.Capparales
                                        APG.Eudicots     C.Caryophyllidae
                                                                                                      C.Caryophyllales        C.Cactaceae
                                                                                                                             APG.Cactaceae


                                                                             APG.Caryophyllales      APG.Polygonaceae       C.Caryophyllaceae                                  Nodes
                                                                            APG.CaryophyllidClade     C.Polygonaceae       APG.Caryophyllaceae
                                                        APG.AsteridClade                               C.Polygonales                                 C.Oleaceae                 C           15
                                                                                                                                                    APG.Oleaceae
                                                                               APG.Ericaceae                                                                                congruent       42
                                                                                APG.Ericales           APG.Lamiales         C.Scrophulariales
                                                                                C.Ericaceae                                                       C.Scrophulariaceae          APG           9
                                                                                 C.Ericales                                                      APG.Scrophulariaceae          Edges
                                                                                                      APG.Asteraceae         APG.Lamiaceae
                                                                                                                              C.Lamiaceae
                                                                                                       APG.Asterales           C.Lamiales                                 is_a (inferred)   12
                                                                                 C.Asteridae           C.Asteraceae
                                                                                                        C.Asterales                                                     overlaps (inferred) 12
                                                                                                                                                                           is_a (input)     69
                                                        APG.BasalEudicots    APG.Ranunculaceae       APG.Caprifoliaceae
                                                        APG.Ranunculales      C.Ranunculaceae         APG.Dipsacales
                     C.Magnoliopsida   C.Magnoliidae                           C.Ranunculales         C.Caprifoliaceae
                                                                                                       C.Dipsacales
                                                        APG.Magnoliaceae
                                                         APG.Magnoliales     APG.Papaveraceae
                                                         APG.Magnoliids       C.Papaveraceae        APG.Asclepiadaceae
                                        APG.Poaceae      C.Magnoliaceae        C.Papaverales         APG.Gentianales
                                         APG.Poales       C.Magnoliales                              C.Asclepiadaceae
                                       C.Commelinidae                                                  C.Gentianales
                                         C.Cyperales                          APG.Orchidaceae
   C.Magnoliophyta    C.Liliopsida       C.Poaceae                             C.Orchidaceae
                                                        APG.Asparagales         C.Orchidales
  APG.Angiosperms    APG.Monocots                                                                     APG.Solanaceae
                                                                                                       APG.Solanales
                                          C.Liliidae                                                   C.Solanaceae
                                                                                C.Iridaceae             C.Solanales
                                                            C.Liliales         APG.Iridaceae

                                                         APG.Arecaceae          APG.Liliaceae
                                                          APG.Arecales           APG.Liliales
                                         C.Arecidae       C.Arecaceae            C.Liliaceae
                                                           C.Arecales

                                                         APG.Alismatales
                                                          APG.Araceae
                                                           C.Araceae
                                                            C.Arales




 Fig. 5. The final one possible world merged solution for reconciling the two flowering plants
classification systems. (green rectangular box=Cronquist; yellow “note” box=APG; grey round
  box=congruent; red concrete line=inferred parent-child relationship by Euler/X; red dotted
                      line=inferred overlapping relationship from Euler/X)
10

    Somewhat ironically, the limitation in this study also lies in the strong inferential
power—in which when a parent node only has one child, the RCC reasoner in Euler/X
will collapse the concepts and merge them as the same node. For example, Euler/X
derived that the family Ericaceae and the order Ericales are exactly the same and
merged Cronquist.Ericaceae, APG.Ericaceae, Cronquist.Ericales, and APG.Ericales as
congruent. However, we argue that this limitation is due to the fact that we have only
chosen some 40 major flower families instead of all 416 families. We could add missing
children or artificial children here, or include the full 416 angiosperms families, but this
is beyond the scope of our study. For the purposes of demonstrating the logic-based
taxonomy alignment approach, our smaller use case is sufficient and more tractable .
    It is also worth noting that domain expert opinions are still needed to differentiate
and lead us to the single solution we are looking for. We foresee our logic-based ap-
proach for aligning KOS as an essential preliminary processing steps and a minimum
viable product before bringing the KOS interoperability alignment problems to the do-
main experts. KOS alignment problems are usually complicated with a slow learning
curve; domain experts, in our case, plant systematists, may not fully comprehend at first
the reason we need to align different KOS. If we approach them directly with two clas-
sifications and ask them one by one what relationships between each concept are, they
will probably feel befuddled by the situation. Once we have the Euler/X-generated pos-
sible worlds in the first round of alignments, whether a few, tens, hundreds, or even
thousands of PWs, the alignment problem will become concrete to the domain experts
and consulting them for validation of the articulations would be much easier.
    This study, we also believe, has further implications on making our classification
systems more “full of beans” (here we take on the positive connotation, meaning full of
energy), meaning that it may open doors to enable semantic interoperability, and enrich
diversity in classification systems when we work with KOS alignments using the logic-
based RCC-5 approach. We believe that in the future we can implement this approach
for semantic interoperability issues among classifications in the information science
community, or even other higher-level KOS such as ontologies.


7      Acknowledgement
The first author wishes to thank Dr. Stephen R. Downie for the wonderful introduc-
tion to plant systematics. This research is the outcome of the course project of IB335
and the Independent Study taught by Dr. Downie. The authors also thank Dr. Nico M.
Franz and Ms. Ly Dinh for support and kind feedback on this research.


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