=Paper= {{Paper |id=Vol-3009/paper5 |storemode=property |title=Metadata-based Term Selection for Modularization and Uniform Interpolation of OWL Ontologies |pdfUrl=https://ceur-ws.org/Vol-3009/paper5.pdf |volume=Vol-3009 |authors=Xinhao Zhu,Xuan Wu,Ruiqing Zhao,Yu Dong Yizheng Zhao |dblpUrl=https://dblp.org/rec/conf/kr/ZhuWZDZ21 }} ==Metadata-based Term Selection for Modularization and Uniform Interpolation of OWL Ontologies== https://ceur-ws.org/Vol-3009/paper5.pdf

Metadata-based Term Selection for Modularization and
Uniform Interpolation of OWL Ontologies

Xinhao Zhu2 , Xuan Wu1,2 , Ruiqing Zhao2 , Yu Dong2 , and Yizheng Zhao1,2
1
National Key Laboratory for Novel Software Technology, Nanjing Univeristy, China
2
School of Artificial Intelligence, Nanjing University, China

Abstract. This paper explores the problem of selecting good terms as seed sig-
nature for abstraction of OWL ontologies. Existing methods generate seed signa-
tures based on geographic connections, which is far from sufficient to produce a
satisfactory abstract. This restricts the reusability of OWL ontologies from the as-
pect of knowledge management. In this paper, we propose a signature extension
approach to generate seed signatures for modularization and uniform interpola-
tion of OWL ontologies, both of which are ontology abstraction techniques. The
approach establishes the semantic relevance of terms by taking into account as
much as possible metadata information of an OWL ontology, and computes a
numerical value to measure the relevance of terms using their embedding trans-
formed based on a so-called OWL2Vec* framework. An empirical evaluation
of the approach shows that the proposed method significantly outperforms other
term selection baselines in making accurate selections. Besides, a case study on
ontology abstraction tasks shows that modularization tools can make more com-
plete and precise abstractions using the signature extended by our method.

Keywords: OWL Ontology · Term Selection · Modularization · Uniform Inter-
polation

1 Introduction
Because of the heterogeneous nature of web resources, ontologies developed for the se-
mantic web are typically large, sometimes monolithic, and knowledge modelled therein
is rich and covers multiple topics. This may however restrict the reusability and inter-
operability of ontologies in real-world application scenarios, since large ontologies can
be difficult to manage, unwieldy to manipulate, and moreover costly to reason about.
Consider an ontology reuse use case where an ontologist wants to import a football
ontology into a growing sports knowledge base. Currently the only well-established on-
tology concerning football is the BBC Sports Ontology3 , which, however, publishes
data about all types of competitive physical activities, pertaining not only to the topic of
football. Importing the whole ontology into the knowledge base is not difficult from an
engineering perspective, but as one can expect, many web services upon the knowledge
base such as search, querying, retrieval, which typically involve extensive reasoning,
3
https://www.bbc.co.uk/ontologies/sport
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons Li-
cense Attribution 4.0 International (CC BY 4.0).
Metadata-based Term Selection 123

may become problematic, as too much irrelevant information has been, automatically
yet unnecessarily, introduced. Such information makes no contribution to the formal-
ization of the information about football but increases the computational cost.
A straightforward way to tackle these challenges of reusability and interoperability
is to extract a fragment of an ontology that can behave in the same way as the original
ontology in a specific context, but is significantly smaller. In the above case, this means
to extract from the BBC Sports Ontology a fragment that contains sufficiently many
logical statements to summarize all knowledge about football. Ideally, this fragment
should be as small as possible.
Two logic-based approaches have been developed for computing fragments of on-
tologies. One is based on modularization [5,9,12,8,2,14], which seeks to identity from
an ontology a subset (module) that preserves several reasoning tasks for a sub-vocabulary
of the ontology, namely a seed signature.4 The other is uniform interpolation [17,15,6,16],
which computes a more compact representation of a module of an ontology which pre-
serves the underlying logical definitions of the terms in the seed signature.
As one could expect, the quality of extracted fragments depends largely on the seed
signature fed to modularization and uniform interpolation procedures. We may say that
a fragment is complete if it covers all essential information about the topic of interest,
and a fragment is precise if it is complete and in addition, it does not include too much
irrelevant information about the topic of interest. More specifically, if we selected as
seed signature too few terms to summarize all materials of the topic, we would lose
important information that a user may be interested in, and if we selected as seed sig-
nature too many terms with some of them not strongly relevant to the topic, we would
include too much additional information. Importing more information can also change
the definitions of the terms in the original ontology [9].
Nevertheless, very little attention has been paid to the problem of term selection for
ontology extraction. Chen et al. [2] have proposed a signature extension algorithm to
generate seed signatures for ontology modularization. The idea is to (1) fix a primitive
seed signature Σ, often containing several domain expert-suggested terms, and (2) ex-
tend Σ with new terms collected from the axioms which contain the current Σ-terms.
This step is iterated until no new terms can be added to Σ. One may understand this
as: if two people p1 and p2 live together in a house h1 on an island, then they are rele-
vant and team up as Σ = {p1 , p2 }, and if there exists a road connecting h1 with another
house h2 , then the people living in h2 are collected into Σ. Iteratively, the same strategy
applies to the entire island, and in the end, Σ will probably have collected all habitants
on the island. However, a person who lives on another island will never be collected by
Σ since there is no road connecting two islands; islands are geographically isolated.
Evidently, following this signature extension strategy one must obtain a larger seed
signature with which, a more informative fragment will be produced, but we may argue
that the seed signature obtained in this way, i.e., using a signature extension algorithm
based merely on geographic connections, could hardly yield a complete fragment. Our
argument is that: the relevance between a term and the expanding seed signature should
be evaluated based on a consideration of all metadata of the participating terms in the
context of the host ontology, rather than based merely on their geographic connections.
4
A signature of an ontology is the set of all concept and role names in the ontology.
124 Xinhao Zhu, Xuan Wu, Ruiqing Zhao, Yu Dong and Yizheng Zhao

Fig. 1: A snippet of a multi-domain ontology

Consider a scenario where an ontologist wants to extract from a multi-domain on-
tology a fragment that describes football and closely related information; see Figure 1.
With the central term “Football” being selected as a single seed in the primitive signa-
ture, an extension Σ = {Football, BallGame, Sports, Player, FootballPlayer}
is obtained using the above signature extension algorithm. Terms in other domains such
as MentholSpray will not be collected in Σ, because it is geographically isolated
from the domain of Sports. However, the annotated information of MentholSpray ex-
plains that “MentholSpray can be used as pain reliever for sports players”. In this sense
the term MentholSpray is supposed to be strongly relevant to the topic. Collecting
MentholSpray in the extended signature may enable the expanded knowledge base to
answer queries regarding the treatment of an injury in a football match. This is a good
example showing that the relevance between a term and the expanding seed signature
in the context of the host ontology could be established based on important metadata of
the participating terms, for example, based on their lexical information.
In this paper, we propose a novel term selection approach to discovering semantic
relationships between two isolated groups of terms. The idea is to measure the rele-
vance of non-Σ terms with Σ terms based on their D-dimensional vector representation
computed from important metadata of the ontology using OWL2Vec* [3], a random
walk- and word embedding-based OWL ontology embedding framework that encodes
the semantics of OWL ontologies in a vector space by taking into account their graph
structure, lexical information, as well as the logical constructors used therein. The work
is intended to enhance existing logic-based ontology abstraction techniques as practical
tools for many ontology-based knowledge processing tasks by exploiting non-logical
approaches to facilitate this transfer. Previously, not much work has considered tightly
coupled logical and data-driven techniques and exploited the complementary strengths
of them to open up an application pipeline. Our empirical evaluation showed that the
proposed approach significantly outperformed other term selection baselines in recom-
mending good seed signatures, and with this approach, more precise fragments could
be produced using one modularization and one uniform interpolation tool.
Metadata-based Term Selection 125

2 Metadata-based Term Selection
For space reasons, we have to assume readers’ familiarity with the notions of ontology
modularization [9] and uniform interpolation [16]. Our term selection approach ac-
commodates ontologies described in OWL 2, which are based on the description logic
SROIQ [11]; see the Description Logic Handbook [1] for a detailed description of the
syntax and semantics of description logics.
Arguably, most topics can satisfactorily be summarized or defined by a set of con-
cept names, but do not depend too much on role names. Hence, in this paper, we only
consider the seed signature to be a set of concept names.
The signature sig(O) of an ontology O is the set of all concept names in O. Given
an ontology O and a seed signature Σ ⊆ sig(O) containing a single or a few concept
names suggested by domain experts or simply selected by users, which are believed to
be the central term or terms that can best summarize the topic of interest, our approach
computes an extension Σ 0 of Σ in three steps, namely concept representation learning,
computing relevance value, and signature extension based on relevance value. Σ 0 is the
seed signature to be fed to modularization and uniform interpolation procedures.

2.1 Concept Representation Learning
The first step is to transform all concept names A in O into D-dimensional vectors in
a vector space where the relevance of each concept name (to Σ) is computed based on
important metadata of O.
Our concept representation learning model is based on OWL2Vec* [3], an ontology
embedding framework, which computes the vector representations for concept names
in OWL ontologies as expressive as SROIQ. OWL2Vec* computes the embedding
of an OWL ontology based on a corpus of sequences of tokens, which are encoded
from the metadata of the ontology. Such metadata includes the graph structure of the
ontology, i.e., an RDF graph (a set of RDF triples) converted from the OWL ontology
by OWL2Vec*, the so-called lexical information about the ontology, i.e., annotations,
and the so-called logical information about the concepts and roles in the ontology, i.e,
subsumption, equivalence, disjointness, etc.
We note that OWL2Vec* was not meant for term selection tasks, so we make mod-
ifications to the original OWL2Vec* model to maximize the performance of the down-
stream term selection models. In particular,we designed a fine-tuning process to further
improve ontology embedding, which was task-specific and further discussed in section
3. In the end, every concept name A is represented as a D-dimensional vector eA .

2.2 Computing Relevance of Concept Names w.r.t Σ
The second step is to compute the relevance value of every (non-Σ) concept name A in
O w.r.t. Σ. The computation is based on the relative distance of e A to its nearest seed
neighbour (the nearest seed name) in the vector space. The range of the relevance value
is [0, 1] with 1 standing for the strongest relevance and 0 for the weakest relevance. The
relevance value is computed by a newly developed algorithm called Nearest Neighbor
Ranking algorithm (NN-RANK), shown in Algorithm 1.
126 Xinhao Zhu, Xuan Wu, Ruiqing Zhao, Yu Dong and Yizheng Zhao

Algorithm 1 Nearest Neighbour Ranking
Input: A set of concepts NC , A set of seed signatures Σ s.t. Σ ⊆ NC ,
A set of concept embedding {eA : A ∈ NC },
A distance function d : RD × RD → [0, ∞].
Output: A relevance function f : NC → [0, 1],

1: Let g be a mapping of NC → [0, ∞].
2: for all A ∈ NC do
3: g(A) := ∞
4: for all A0 ∈ Σ do
5: g(A) := min (d (eA , eA0 ) , g(A)).
6: end for
7: end for
8: Let f be a mapping of NC → [0, 1].
9: for all A ∈ NC do
10: Find i, s.t. A has the i-th smallest g(A) in NC .
11: f (A) := 1 − (i − 1)/|NC |.
12: end for
13: return f

NN-RANK first computes the distance from each concept name to each seed name
in the vector space. In principle, many distance functions d : RD × RD → [0, ∞] can
be used to achieve this, but the Consine distance, formulated as
eA · eB
d(eA , eB ) = 1 −
keA k2 keB k2

has made the best measure of relevance in our experiments. |Σ| distance values are
computed in this way for each concept name A, while the smallest distance value, which
denotes the shortest distance, is identified as a valid distance value of A to Σ. NN-
RANK then sorts all concepts names in O by their valid distance value. Concept names
with smaller valid distance values are considered to be semantically more relevant to
the seed signature, and thus to the central topic. These valid distance values (and the
corresponding concept names) are then uniformly distributed between 0 and 1. The
result is the relevance value of each A w.r.t. Σ.

2.3 Relevance-based Seed Signature Extension

A natural question arises: how to use the computed relevance values to guide the selec-
tion of terms for ontology abstraction? Upon different application demands, the strate-
gies may vary. Without a well-acknowledged gold standard, a feasible solution could
be to measure the “degree” of relevance and define to what degree the relevance is a
concept name can be thought of as “relevant” to the seeds in Σ. In this work, we use a
threshold σ at the scale of 0 to 1 to denote the “degree” of relevance. Our approach ex-
tends the primitive seed signature Σ by adding to Σ the concept names with relevance
value no less than σ. The result is Σ 0 = Σ ∪ {A | A ∈ sig(O) ∧ f (A, Σ) ≥ σ}.
Metadata-based Term Selection 127

Lemma 1. Given any OWL ontology O in SROIQ and a primitive seed signature
Σ ⊆ sig(O) with n = | sig(O)| and k = |Σ|, our term selection approach always
computes an extended seed signature Σ 0 such that Σ ⊆ Σ 0 in O(n log n + kn) time.

3 Empirical Evaluation of NN-RANK
In this experiment, we used NN-RANK to predict SNOMED CT Refset components.
The aim was to show that the algorithm could enrich a given primitive seed signature Σ
with concept names highly relevant to the initial seeds (in a vector space). The experi-
ment was conducted on a work station with an Intel Xeon CPU @2.60GHz and 32 GB
memory.
SNOMED CT5 is currently the most comprehensive, multilingual clinical health-
care ontology in the world. A SNOMED CT Refset6 is a collection of SNOMED CT
components sharing specific characteristics (e.g., a specific domain). An example of
SNOMED CT Refset is the Malaria refset released by the National Resource Centre for
EHR Standards in India, which includes findings, disorders, and organisms related to
Malaria. Arguably, the refset published officially by a group of ontology engineers and
domain experts, can be considered as a complete and precise standard of an Malaria
abstract of SNOMED CT.
Our task was to predict concepts in SNOMED CT Refsets based on a seed signature
(randomly or manually) selected from the refsets. This task was designed to fit with
realistic scenarios where we needed to develop a new refset with least intervention
from domain experts. We assumed that refsets developed by the domain experts were
complete and precise fragments, containing concepts that were highly interconnected on
the semantic level (e.g., in the same clinical domain). Therefore, the task of predicting
SNOMED CT Refset components could be used to evaluate the performance of term
selection models.
To better position our algorithm, we compared NN-RANK with two other term se-
lection strategies, namely, a strategy adapted from locality-based modularization [10]
(denoted as Star-modularization), and the signature-extension based on geographic con-
nections [2] (denoted as Sig-Ext, configured with depth d). We treated them as baselines.
The idea of the locality-based modularity strategy was to take all concept names in the
computed module as the extended signature of the seed. This may not be ideal but
was nevertheless a means to extend the seed signature. In this way, the relevance value
f (A, Σ) of A was 1 if A was in the signature of the computed module, and 0 other-
wise. We also considered a comparison of NN-RANK with Meta-SVDD [7], a model
designed for few-shot one-class-classification problems. Using Meta-SVDD, we learnt
patterns about refsets from existing refsets, in order to enhance its performance in pre-
dicting new refset components.
5
https://www.snomed.org/
6
https://confluence.ihtsdotools.org/display/DOCGLOSS/refset
128 Xinhao Zhu, Xuan Wu, Ruiqing Zhao, Yu Dong and Yizheng Zhao

We considered the International Edition of SNOMED CT (version July 2020), which
contains 354,256 concepts, 355,214 logical axioms, and 1,506,185 description axioms.
We used two sets of publicly accessible and in-use term collections, NHS refsets7 and
NRC refsets8 , as the target refsets.
The NHS refsets, issued by the National Health Service (NHS) in the UK, offered
from the full Edition of SNOMED CT a set of components defined by a particular
requirement. The NRC refsets were released by the National Resource Centre for EHR
Standards (NRCeS) in India, which contained 30 standalone refsets covering concepts
related to common diseases.
We adopted two metrics widely used in classification and ranking tasks, namely the
Normalized Discounted Cumulative Gain (NDCG) and the Area under the ROC Curve
(AUC), to evaluate the performance of term selection models. Both measures returned
high values if a model made accurate predictions, i.e. they measured the similarity be-
tween the approximations and the refset components.
Ontology embedding generated by OWL2Vec* on SNOMED CT was used for the
concept embedding, where each concept was represented by a 200-dimensional vector.
Different from the original OWL2Vec* model, we used a fine-tuning process specially
designed for this task, to further improve the ontology embedding. Specifically, refsets
in this process were transformed to documents containing (concept uri, refset identifier,
concept uri) triples, then a Word2Vec model was used to fine-tune the pre-computed
concept embedding on these documents. The fine-tuning process was done in a 10-
fold cross validation manner, which meant that evaluations on any refset is based on a
concept embedding fine-tuned on 90% refsets other than itself.
For NRC refsets, two seed signatures Σr and Σs consisted of K concepts respec-
tively were used throughout the experiment. Σr was randomly selected among all the
refset concepts, while Σs was manually selected with the aim that the K concepts it
contained could describe the topic from different aspects. For NHS refsets, we only
used a different set of Σr generated in the same way. It was crucial to be able to set
the size of the primitive seed signature K accordingly to the application. In realistic
use cases, the seed signature may be manually selected, where smaller K means less
manual cost, so K = 5 is used in the experiments.
We used the OWL API syntactic locality module extraction tool9 as the implemen-
tation of the locality-based module, and the official implementation of Sig-Ext. For
Meta-SVDD, our implementation was based on the source code provided by [4].

3.1 Results and Analysis

The results (mean value ± standard deviation of the two measures) in Table 1 and 2
show that embedding-based methods outperformed logical approaches in the above set-
tings. This was because logical methods were not designed for this task, and it did
not capture lexical information of the ontology, which was crucial in determining the
semantic relevance between concepts.
7
https://dd4c.digital.nhs.uk/dd4c/
8
https://www.nrces.in/resources#snomedct releases
9
https://github.com/owlcs/owlapi
Metadata-based Term Selection 129

Besides, NN-RANK slightly outperformed Meta-SVDD, particularly when using
Σs . We will conduct a case study on the aforementioned Malaria refset to explain the
mechanism and effectiveness of NN-RANK in this task.

Table 1: Results on NHS, NRC refsets using Σr (the higher the better).
Methods NHS refsets NRC refsets
NDCG AUC NDCG AUC
K=1 K=5 K=1 K=5 K=1 K=5 K=1 K=5
Star-modularization 40.93 ± 14.61 47.33 ± 13.36 50.84 ± 1.10 54.73 ± 5.56 49.10 ± 16.23 51.83 ± 14.62 50.64 ± 0.98 54.58 ± 7.82
Sig-Ext (d=1) - 49.14 ± 10.92 - 54.31 ± 5.58 - 55.68 ± 11.06 - 53.60 ± 6.73
Sig-Ext (d=2) - 47.99 ± 11.66 - 54.31 ± 5.58 - 54.31 ± 11.81 - 53.78 ± 6.91
Meta-SVDD - 67.72 ± 23.26 - 91.55 ± 10.43 - 71.65 ± 16.62 - 88.81 ± 8.87
NN-RANK 68.57 ± 20.36 77.93 ± 14.91 92.19 ± 11.19 96.49 ± 5.11 71.32 ± 14.33 77.25 ± 10.03 89.66 ± 8.42 94.29 ± 5.51
NN-RANK + fine-tuning 69.50 ± 20.13 78.76 ± 14.62 93.33 ± 9.57 96.98 ± 4.62 73.57 ± 12.54 80.19 ± 9.14 90.40 ± 8.43 94.79 ± 5.69

Table 2: Results on NRC refset using Σs (the higher the better).
Methods NDCG AUC
K=1 K=3 K=5 K=1 K=3 K=5
Star-modularization 48.85 ± 16.68 50.65 ± 15.26 52.25 ± 14.42 50.82 ± 2.01 53.21 ± 5.53 54.68 ± 7.50
Sig-Ext (d=1) 49.97 ± 15.36 53.42 ± 12.16 55.76 ± 10.48 50.80 ± 1.53 52.14 ± 3.89 53.34 ± 5.81
Sig-Ext (d=2) 49.56 ± 15.82 52.33 ± 13.06 54.38 ± 11.36 50.87 ± 1.60 52.28 ± 4.01 53.48 ± 5.93
Meta-SVDD 71.28 ± 12.25 74.91 ± 16.48 75.24 ± 13.73 72.4 ± 16.23 86.83 ± 10.05 92.01 ± 6.45
NN-RANK 79.77 ± 11.79 83.67 ± 10.74 84.83 ± 9.95 94.07 ± 5.11 96.09 ± 3.73 96.64 ± 3.09
NN-RANK + fine-tuning 80.39 ± 12.02 84.41 ± 10.95 85.53 ± 10.20 94.65 ± 5.01 96.49 ± 3.73 96.97 ± 3.06

Figure 2 shows the distribution of the Malaria refset components and other SNOMED
CT concepts in a 2-dimensional vector space. As illustrated in the figure, refset compo-
nents tended to form a number of minor clusters, with each containing some highly
semantically relevant concepts. The whole refset was composed of several concept
clusters instead of a giant cluster. This meant that when two seed concepts A1 and
A2 were given, any concept A that was similar to A1 or A2 , i.e. d(eA , eA1 ) < or
d(eA , eA2 ) < with being a small value greater than 0, were more likely to be a ref-
set component compared to another A which was similar to the average of eA1 and eA2 ,
i.e., d (eA , (eA1 + eA2 )/2) < . NN-RANK was designed to fit in this multi-clusters
pattern, and achieved better performance compared to other models utilizing concept
embedding.
The performance of NN-RANK could be significantly enhanced when seed signa-
tures described the topic from different aspects. For a high quality primitive seed sig-
nature like Σs , an increased seed signature size would generally led to more accurate
selection results.

3.2 Time Efficiency
For the current setting of N = 354, 256, K = 5, D = 200 and using Cosine distance
as the distance function, NN-RANK generated Σ 0 within 5 seconds. For comparison,
130 Xinhao Zhu, Xuan Wu, Ruiqing Zhao, Yu Dong and Yizheng Zhao

it usually takes minutes to hours for other approaches (e.g., Star-modularization and
Sig-Ext) to compute on a large-scale ontology like SNOMED CT, and five minutes for
the Meta-SVDD model to converge in the same setting.

It is true that our approach takes hours to build embedding vectors on SNOMED
CT, but this cost is acceptable in real-life scenarios since the training is conducted only
once but can be meaningfully used many times and forever. Also, the training time can
be adjusted. When the ontology contains less than 100K logical and annotation axioms,
it is typically less than one hour.

Fig. 2: Distribution of malaria refset components and other SNOMED CT concepts ( 170 concepts
from the malaria refset and 1700 random concepts outside of the refset). Each point corresponds
to a SNOMED CT concept, whose colour shows its relevance with the seed signatures computed
by NN-RANK (the higher, the deeper), and shape denotes its type (cross for being refset compo-
nents, and circles for not). Seed concepts are depicted as blue stars accompanied with tags. The
mappings between tag and label are: A - Malaria (disorder), B - Allergy to primaquine (finding),
C - Accidental pyrimethamine poisoning (disorder), D - Malaria outbreak education (procedure),
E - Antimalarial drug adverse reaction (disorder)
Metadata-based Term Selection 131

4 Case Study: Ontology Abstraction
In this part, we explored how input signature extended by NN-RANK benefits differ-
ently between modularization and uniform interpolation in the OWL ontology abstrac-
tion task.
As we need ontology having enough metadata to test the effectiveness of term se-
lection method, we considered HeLiS10 , an ALCHIQ(D) ontology integrating knowl-
edge about food and activity from a nutritional point of view. The experiment was based
on HeLiS v1.10 which has 172,213 axioms, 277 concepts, and 50 roles.

4.1 Setup Details

First, we randomly generated 10 concept subsets from sig(OHeLiS ) with the size of
subsets ranged from 1 to 5. These randomly generated concept sets, denoted as Σr ,
could be the approximations of seed signatures around random topics. Then NN-RANK
returned the ordered sets Σ 0 .
As the abstractions in real-life are usually small in size, we chose the top 10%
of Σ 0 (i.e., set the threshold as 0.9) to be the input signature for modularization and
uniform interpolation. We used UI-FAME [18] to compute uniform interpolants, and
Star-modularization to compute locality-based modules as they are publicly accessible.
Both preserved full logical entailments of the input signature Σ 0 in OHeLiS [10,13].
Then the abstraction results computed by these two tools with the input of Σ 0 (denoted
as Σ 0 +UI-FAME, Σ 0 +Star-modularization) were assessed with four metrics: module
size |M|, module inherent richness InhRich, module intra distance IntraDist and mod-
ule cohesion Cohesion. A module with relative smaller size, higher inherent richness,
relative smaller intra distance, and higher cohesion was said to be more compact. We
also test Σr +Star-modularization and compared it with Σ 0 +Star-modularization.

4.2 Results and Analysis

We compared Σ 0 +UI-FAME and Σ 0 +Star-modularization to see the effectiveness of
NN-RANK to different abstraction methods. From table 3, we can see that UI-FAME
generated more compact abstractions. Besides, UI-FAME was sensitive to the input
signature. These results make sense because locality-based modularization introduced
other terms which were not in Σ 0 but uniform interpolation stuck to Σ 0 . Experiments
with thresholds setting as 0.3, 0.5, and 0.7 show that the size of Σ 0 did not affect the
compactness of the locality-based module abstraction.
Term selection allowed users to extend the seed signature in an adjustable way. For
uniform interpolation, it is a key step to select suitable terms for the specified topic, be-
cause the semantics of the topic is mainly captured by the input terms. We observe that
once if the input terms were not sufficient enough for uniform interpolation, the module
could be very small, containing many meaningless axioms like A v > or concept asser-
tion axioms. NN-RANK+UI-FAME generated knowledge highly relative to the topic.
For instance, in Table 4, the topic was “SpecialBread”. The related axioms in OHeLiS
10
https://horus-ai.fbk.eu/helis/
132 Xinhao Zhu, Xuan Wu, Ruiqing Zhao, Yu Dong and Yizheng Zhao

Table 3: Module compactness Evaluation (Use top 10% Σ 0 as input. |M| is the sum of quantities
of concepts, roles and individuals in M . InhRich: the average number of subclasses per class.
IntraDist: the overall distance between the entities in the module. Cohesion: the extent to which
entities are related to each other in the module.)
Metrics K=1 K=5
Star-modularization UI-FAME Star-modularization UI-FAME
|M| 171 ± 14 20 ± 7 174 ± 15 18 ± 8
InhRich 2.92 ± 0.12 2.1 ± 1.25 4.08 ± 0.17 3.75 ± 0.49
IntraDist 49683.90 ± 94.61 618.75 ± 617.87 49798.70 ± 278.77 289.50 ± 344.26
Cohesion 0.08 ± 0.01 0.19 ± 0.09 0.08 ± 0.00 0.15 ± 0.10

Table 4: Term selection for SpecialBread topic in HeLiS
Σr {SpecialBread}
Of ragment SpecialBread v Bread
{SoyBread, OliveBread, MilkBread, OilBread, RyeBread}v SpecialBread
Σ 0 @10 SpecialBread, Bread, WhiteBread, PizzaAndFocacciaBread,
OlivesAndOliveProducts, SoyProducts, LegumesAndLegumeProducts,
WheatFlour, WholeWheatFlour, MilkAndDairyProducts

were contained in Of ragment . Clearly, “SpecialBread” had five individuals. Besides,
these individuals had no other super-classes except “SpecialBread’. As commonsense
knowledge, “OliveBread” can be “OlivesAndOliveProducts”, “SoyBread” can be
“SoyProducts”, “MilkBread” can be “MilkAndDairyProducts”, which were miss-
ing in OHeLiS . So without the extension of NN-RANK, these related concepts could not
be preserved in Σr + Star-modularization or Σr + UI-FAME. While NN-RANK could
preserve them according to that “OlivesAndOliveProducts”, “SoyProducts”, and
“MilkAndDairyProducts” were lexically close to the individuals of the topic concept
“SpecialBread”.
To sum up, with NN-RANK modules and uniform interpolants produced more com-
plete fragments. In addition, Σ 0 +uniform interpolation produced more precise frag-
ments than Σ 0 +modularization.

5 Conclusion and Future Work
This paper makes a preliminary attempt to address the problem of extending the given
seed signature with new terms selected sophisticatedly through embedding-based com-
putation of important metadata of an OWL ontology. An evaluation of the approach on
a predication task of a SNOMED CT refset shows that our approach makes accurate
selections compared with other term selection baselines. A case study shows that high-
quality modules and uniform interpolants of OWL ontologies can be produced using
our term selection approach.
Metadata-based Term Selection 133

The absence of standardized benchmarks remains the main bottleneck in evaluating
the performance of term selection methods. Hence, a number of pre-defined question
answering instances that are generated based on the input ontology might be helpful in
deciding the completeness and precision of the generated abstracts of OWL ontologies.
For a problem Q that can be answered by querying an ontology O, a satisfactory abstract
M of O regarding a input signature Σ should be able to answer Q if Q is relevant to
Σ, and should not be able to answer Q if Q is not relevant to Σ.
Besides, the current experiments only considered concepts. Roles will also be con-
sidered in the future work.

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