Formal Concept Analysis (FCA) comes with a range of relevant techniques for knowledge analysis, such as conceptual structures or implications. The Duquenne-Guigues basis of implications provides a cardinality minimal set of non-redundant implications. The concern of a domain expert is to discover new knowledge within this implication set. The objective of this prospective paper is to collect and discuss the di erent patterns of implications extracted from a dataset on plants used in medical care or consumed as food. We identify 16 patterns combining 3 types of knowledge elements (KE). The patterns highlight redundant KEs, or KEs of little interest, in particular, those corresponding to plant taxonomy, as it is familiar knowledge for the experts. Removing these KEs from the implications would make them tacit. We suggest a postprocess for cleaning up the implications before reporting them to the experts. In addition, we discuss the di erent patterns and how an implication classi cation based on patterns could help the experts.
Formal Concept Analysis (FCA) is a mathematical framework based on lattice
theory which aims to formalize the notion of concept [
Through DGB building, expert concern is to discover new knowledge within the implication set. Diverse situations can occur. For instance, if an implication is too obvious for the expert, e.g. because it exclusively describes a domain taxonomy, then it presents a too limited interest to be kept in the implication set. This implication therefore becomes a tacit knowledge, while the others remain explicit. In more complex situations, the implication may contain both obvious knowledge elements (KE) and useful KE. In such cases, the obvious part of the implication may become tacit, when the other part may remain explicit.
The objective of this paper is to observe and discuss di erent patterns of implications extracted from a dataset on plants used in medical care or consumed as food. With these patterns, we aim to identify obvious KE included in the implications, and how implications can be simpli ed. The patterns may also provide an opportunity to classify the implications into coherent sets. Section 2 introduces the background and the dataset. Section 3 presents and discusses the preliminary results. Section 4 concludes and draws future work. 2
Background FCA elaborates knowledge, including formal concepts or attribute
implications, on top of a formal context (FC) K = (G; M; I) where G is an
object set, M is an attribute set and I G M . An implication, denoted
by A =) B, is an attribute set pair (A; B); A; B M such that all
objects owning the attributes of A (premise) also own the ones of B (conclusion):
fgj8ma 2 A; (g; ma) 2 Ig fgj8mb 2 B; (g; mb) 2 Ig. There are several types
of implication bases [
This dataset indicates for each plant organism, out of the 600 in the dataset, its species, its genus, its family, and whether it is consumed as food and used in medical care. There is one-to-one mapping between organisms (objects) and Species values (cf. Tab. 1). Species, genera, and families respect a taxonomy which is a 3-level tree structure with this general shape: Species Genus Family; E.g. Species Acorus calamus Genus Acorus Family Acoraceae (see Fig. 1). This taxonomy is a familiar knowledge for the experts. The dataset comprises 600 species from 376 genera and from 98 families.
Formal context built from the dataset A FC describes a set of objects using a
set of Boolean attributes. When the dataset contains a multi-valued attribute,
conceptual scaling can be used to obtain Boolean attributes [
As noticed in [
The implications from DGB Due to the scaling of the attributes Species, Genus, and Family, the FC associated to the dataset has 1078 Boolean attributes, i.e. 600 attributes to inform on the species, 376 on the genus, 98 on the family, and 4 on the medical and food use. For the 600 plant organisms, Table 2 shows that 1168 implications were extracted from this FC. Most of the implications, i.e 1007, are held by one object, and thus are speci c to a plant species. Among the 161 remaining ones, 9 implications are supported by more than 9 objects. The maximum scope, i.e. 35, corresponds to the implication informing that none of the 35 species from the Meliaceae Family, present in the dataset, is consumed (cf. ID 1 in Table 3).
These 1168 implications are formulated using 16 patterns, where a pattern corresponds to the pair (Premise, Conclusion) in which each of the declarative sentence is designed using the SGFp schema (Table 3). This schema is the ordered list of presence of the attributes Species (S), Genus (G), Family (F), food or nofood, medical or no-medical (p), in the declarative sentence. By grouping food, no-food, medical and no-medical, our intent is to focus our analysis on the types of KEs, and not the KEs themselves.
Various combinations of S, G, F, and p can be observed in the premise or the conclusion. For instance, pattern 1 informs on the use of all plants from a family. Pattern 2 provides the taxonomic relation of a genus with a family. Some patterns are more extended, such as pattern 5 that states on the genus of plants from a family with a given use. Three types of KEs were identi ed in the implications. KU type informs on the relationship of a plant, at any taxonomic level, with a use as food or medical care. The second KE type is the Taxonomic relationship type (KT), such as giving the family in the conclusion when the species is indicated in the premise. The third type (KD) corresponds to a KE resulting from the content of the Dataset, which represents a limit in this work. For instance, taxonomic referential web sites list 5 genera from the Piperaceae family 5. As only one is present in the dataset (i.e. Piper), inferring that \a plant from the Piperaceae family is of the genus Piper " is wrong in the real life, but is true in this work as it results from a side e ect of the dataset.
Except for patterns 2 and 6, all the implication patterns include KU (Table 3), suggesting at rst sight that the latter are useful implications for the expert. But attention should be paid on implications combining KU, KT, or KD, and respected by implications with a scope value of 1, meaning that each one is associated to a single plant organism. Pattern 10 (scope 600) only reports information from the context as these rules only describe an organism by its 5 E.g. http://www.plantsoftheworldonline.org/ lists 5 plant genera. attributes. Similarly, patterns 11 and 14 indicate that a given genus or family has only one species in the dataset, the other attributes being those of the species, and these patterns could be considered as containing only KD. Most of the patterns include KT. Including the taxonomy was crucial in this work for FC processing in order to discover knowledge at a higher generic level, but corresponds to a redundancy in the implications.
This preliminary analysis gives directions for pattern and implication postprocessing and classi cation. Some may be speci c to some characteristics of Knomana, such as the fact that attribute species is an object identi er, and some could be generalized to all datasets.
The post-processing may have di erent forms for redundant or evident
information: either removing it, or simply separating it from the rest, so that it
remains written but not distracting. KU, KD, KT can be highlighted in di erent
ways to distinguish them. Highlighting the di erent reasons under redundancy
or evident information (e.g. KT information versus logical redundancy due to the
fact that minimal generators are not used) would be useful. We could consider
removing redundancy only in premise [
Patterns also have to be analyzed. For example, pattern 4 (G -> Fp) could be simpli ed as G -> p, as F is tacit given G. This would change the pattern classi cation (initially KU KT), as it is now reduced to KU.
As regard with implications, a post-process could remove KT from the
implications, corresponding to a tacit knowledge as experts are familiar with the
taxonomy. As the redundancy due to KT may appear in the premise (e.g. the
species and its genus ), in the conclusion, or in both (e.g. a species implies a
family ), the post-process has to consider the implication in its entirety. This
approach di ers with [
KUs are the explicit KEs investigated by the expert and thus have to be put forward. KDs present a particular situation in the implications as they result from a lack of knowledge in the dataset. Pattern 6 has to be considered carefully as it contains only KD. Thus, the experts have to be alerted of KD presence to consider this aspect in the dataset analysis.
A classi cation of implications based on patterns seems to us relevant for presenting them to the expert by groups having a coherent meaning: E.g. implications providing information on the diversity of some plant families in the dataset or pure information on the One Health Approach. Depending of the number of rules in some categories, a classi cation may have a signi cant impact for the expert, e.g. discarding or at least separating rules from pattern 10 distinguishes 600 rules that only recall initial data. We also guess that if a postprocessing is made, the way it is made has to be noti ed to the expert and it should be indicated if this is reversible operation.
Finally, literature on association rules also faced the issues of extension of
non-redundant rules [
This paper identi es 3 types of knowledge elements and 16 patterns that constitute the implications from the Duquenne-Guigues basis on a formal context. Each implication needs a speci c consideration before being presented to the expert. For instance, a post-process can be conducted to remove tacit knowledge elements from implications, which may drive to delete some of them.
In a future work, we will study how the di erent patterns can be used to display implications to experts by categories, that may help them to focus on di erent aspects of the dataset. For instance, the user may focus on knowledge elements related to some plant families in the dataset, or pure knowledge elements on the plant uses at the family level.
This work is a preliminary study to the analysis of the Duquenne-Guigues basis of implications resulting from a Relational Context Family of the Knomana knowledge base. The general objective is to contribute in the decision support process to identify plants that could be used by farmers to control pest. These pesticidal plants will be an alternative to pesticide and antibiotics, considering the One Health approach. Using this approach, one must be aware of the multiuses of these plants to prevent the intentional e ects on the animals, the humans, and their environment.
In a more general perspective, it would be relevant to examine how the forms of post-processing, ltering and classi cation of patterns and rules can be generalized in order to be able to apply these approaches to other datasets, more particularly when several taxonomic relations are involved. Acknowledgments. We warmly thank the reviewers for their comments. Part of the discussion has been notably improved thanks to their relevant remarks. This work was supported by the French National Research Agency under the Investments for the Future Program, referred as ANR-16CONV-0004.