Term Selection for Abstraction of OWL Ontologies
Xuan Wu

Yu Dong

Yizheng Zhao∗

State Key Laboratory for Novel
Software Technology, Nanjing
University
China
wuxuan@smail.nju.edu.cn

State Key Laboratory for Novel
Software Technology, Nanjing
University
Chinadongy@smail.nju.edu.cn

State Key Laboratory for Novel
Software Technology, Nanjing
University
Chinazhaoyz@nju.edu.cn

ABSTRACTThis paper attempts to address the challenge of effectively selecting suitable terms (i.e., concept names) as seed signatures for theabstraction of OWL ontologies. Established methods for generating
seed signatures rely predominantly on geographical connections, apractice that proves to be inadequate in yielding satisfactory abstractions. This limitation consequently curtails the practical reusabilityof OWL ontologies within the broader context of knowledge management. To overcome these limitations, this paper introduces anovel approach called “signature extension”. This approach serves
the dual purpose of generating seed signatures for “modularization”
and “uniform interpolation” of OWL ontologies, both of which arepivotal ontology abstraction techniques. The signature extension
approach is designed to establish the semantic relevance of concept
names by harnessing the treasure trove of metadata information
available within a given OWL ontology. Specifically, it quantifies
the relevance of these names through a numerical measure, which
is derived from their embeddings transformed using the OWL2Vec*
framework. Empirical evaluations conducted on this approach unequivocally demonstrate its superior performance when comparedto other established methods for term selection. In addition, a comprehensive case study on ontology abstraction tasks shows thatmodularization tools can create more comprehensive and precise
abstractions when utilizing the signatures extended through our
proposed approach.

CCS CONCEPTS• Theory of computation → Description logics; Automatedreasoning; • Computing methodologies → Ontology engineering.

KEYWORDS
Description Logics; Ontologies; Uniform Interpolation; Forgetting
ACM Reference Format:
Xuan Wu, Yu Dong, and Yizheng Zhao. 2023. Term Selection for Abstractionof OWL Ontologies. In Proceedings of The 12th International Joint Conference∗ Yizheng Zhao is the corresponding author of this paper.

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https://doi.org/10.1145/3583780.3614771

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New York, NY, USA, 9 pages. https://doi.org/10.1145/3583780.3614771

1

INTRODUCTION

Given the inherent diversity of web resources, ontologies designed
for the semantic web—such as OWL ontologies [3]—tend to be extensive, capturing knowledge across a broad range of topics [13].
However, their scale and breadth can impede reusability and interoperability in practical applications. This challenge stems chiefly
from the difficulties in managing and manipulating large, complex
ontologies, which can become cumbersome and demand substantial
computational resources during the reasoning process. A promising approach to mitigate these issues is to distill a fragment froman ontology that replicates the original ontology’s functionality
within a specific context, yet is significantly smaller in size. The
ultimate goal is to optimize the size reduction of this fragment to
the maximum extent possible.
Two logic-based approaches have been developed for extracting meaningful fragments of ontologies. One approach, known as
modularization [5, 8, 10, 11, 15, 17], focuses on identifying a syntactic subset, namely a module, within an ontology. This module
is carefully selected to maintain the validity of several reasoning
tasks within a specific sub-signature of the ontology, referred toas a seed signature. The second approach, referred to as uniform
interpolation [19, 23, 24], is concerned with the computation of amore compact representation of a module within an ontology. This
refined module, called a uniform interpolant, retains the underlying
logical definitions of the terms within the seed signature. To sum
up, these two approaches offer distinct strategies for computing
ontology fragments, and their utilization is contingent on specificuse cases and requirements in the context of ontology engineering.
As one might expect, the quality of extracted fragments significantly relies on the seed signature used in the modularization anduniform interpolation procedures. We can define a fragment as“complete” if it encompasses all essential information pertaining
to the topic of interest. A fragment is considered “precise” whenit meets the criteria of completeness and, additionally, avoids incorporating excessive irrelevant information concerning the topic.
To elaborate, selecting too few terms for the seed signature could
result in the loss of vital information that a user might find valuable.
Conversely, choosing too many terms, some of which are weakly related to the topic, would introduce excessive additional information.
Furthermore, importing more information can alter the definitionsof terms within the original ontology, potentially undermining its
coherence and consistency [11].
Nonetheless, there has been limited focus on the problem of term
selection when it comes to extracting fragments of ontologies. Chenet al. [5] proposed a “signature extension” approach to generating
seed signatures as input to ontology modularization procedures.
The idea behind this approach is twofold:
Step (1) Start with a “primitive seed signature” Σ, typically containing several terms suggested by domain experts;
Step (2) Extend Σ by including new terms found in the axioms
that involve the existing Σ-terms.
This process is repeated until no additional terms can be added toΣ. To illustrate this, consider the analogy of people living on an
island: if two individuals, denoted as p_1 and p_2, reside together
in a house h_1 on an island, they are considered “relevant” and areincluded in Σ = {p_1, p_2}. If there exists a road connecting h_1
to another house h_2, the individuals in h_2 are added to Σ. This
iterative strategy is applied throughout the entire island, resultingin Σ eventually encompassing all residents on the island. However,
it is important to note that a person living on a different island will
never be included in Σ due to the absence of a connecting road;these islands are “geographically isolated”.
Clearly, when applying this signature extension approach, one
would acquire a larger seed signature, and consequently, a more
informative fragment. However, it can be argued that the seed signature obtained from this approach, which relies solely on geographic
connections, may struggle to produce a “complete” fragment. This
argument stems from the belief that assessing the “relevance” between a term and the expanding seed signature should encompass
a comprehensive evaluation of all metadata associated with theparticipating terms within the framework of the host ontology.
This perspective emphasizes the need to consider factors beyond
geographic connections when determining term relevance in thiscontext.

Figure 1: A snippet of a multi-domain ontology

Consider an ontologist working with a medical ontology that
contains information about various medications and their applications. Within this ontology, there is a term called “MentholSpray”
that is part of the medical domain. Initially, when selecting the seedsignature for abstraction, the ontologist focuses on terms related
to general healthcare but does not include “MentholSpray” in theprimitive signature because it is not explicitly associated with sports
or football. However, upon further examination of the ontology’s
metadata, it becomes evident that “MentholSpray” is often used totreat sports-related injuries, especially in the context of football. The
metadata includes notes from healthcare professionals indicatingthat “MentholSpray” is commonly prescribed for pain relief in football players after matches or during recovery from sports-related
injuries. In this scenario, despite the initial geographic isolationof “MentholSpray” from the sports domain, its strong relevance tothe topic of football emerges when considering the comprehensive
metadata. Consequently, including “MentholSpray” in the extended
signature could significantly enhance the ability of the ontology
fragment to answer queries related to pain management in football, showcasing the importance of metadata-driven term relevanceassessment within the host ontology’s context.
The metadata of OWL ontologies comprises a wealth of semantic
information and other critical information, which may encompass
potential semantic relationships among concepts within these ontologies. Effectively leveraging this information can assist in theestablishment of connections within concepts that extend beyond
the boundaries of the logical components defined in the ontologies.
However, given the multi-dimensional nature of semantic information contained within metadata, the current consensus has shifted
toward mapping this information into vector representations. During the process of term selection, the absence of supervision signals
renders the similarity between vector representations contingent
upon the choice of distance function [4]. It is crucial to stress thatthe main contribution of this work does not lie in delineating thesimilarity function. Rather, our focus is centered on integrating explicit metadata semantic information within logic-based ontology
modularization frameworks, thereby enhancing their functionality.
In this paper, we introduce a novel approach to term selection
aimed at uncovering semantic relationships between two distinctgroups of terms. Our method involves assessing the relevance ofnon-Σ terms to Σ terms based on their D-dimensional vector representations, which are computed using essential metadata fromthe ontology. These vector representations are generated using
OWL2Vec [6], an ontology embedding framework that leverages
random walk and word embedding techniques. OWL2Vec encodes
the semantics of OWL ontologies in a vector space, taking into
account various aspects, including the ontologies’ graph structure,lexical information, and logical constructs. The primary objectiveof this work is to enhance the practical utility of existing logicbased ontology abstraction methods for a wide range of ontologybased knowledge processing tasks. This enhancement is achievedby incorporating non-logical approaches to streamline the process.
Historically, there has been limited exploration of the synergies between logical and data-driven techniques and how they can leverageeach other’s strengths to establish a robust application framework.
Our empirical evaluation demonstrates that our proposed approach
outperforms conventional term selection baselines when recommending suitable seed signatures. By adopting this approach, we
can generate more precise ontology fragments using two established modularization and uniform interpolation tools.

2 PRELIMINARIES
2.1 Description Logic and OWL
An ontology fixes a vocabulary of terms (called classes, which aresets of instances characterized by some shared properties of its instances) relevant to a subject domain, and specifies (as a formal description of domain knowledge) constraints among the classes andthe relationships holding between classes by logical statements [22].
The logical statements on memberships of data elements (called
individuals) in classes or relationships between individuals form abase of facts, i.e., a database [20]. When we speak of ontology, we
think only of the knowledge specifying the constraints among theclasses and the relationships. We include both the constraints andthe facts under the term knowledge base. In DLs, classes are called
concepts and relationships are called roles.
Modern ontologies are formulated in the OWL 2 Web Ontology Language (OWL 2 for short) [18] based on description logics(DLs) [1, 2], which are a successful family of knowledge representation languages. OWL 2 introduces different profiles, each withvarying levels of expressiveness to cater to different use cases andcomputational complexities. Among the most commonly used profiles are OWL 2 EL (Description Logic EL++), OWL 2 QL (Query
Language), and OWL 2 RL (Rule Language). These profiles allow ontology developers to choose the appropriate level of expressivenessand reasoning complexity for their specific applications, balancing
computational efficiency with modeling capabilities. OWL 2 Full is
by far the most expressive of the profiles in OWL 2, which corresponds to the DL SROIQ [14]. Our term selection approach does
not require a specific level of expressiveness (i.e., logic-independent)
and is universally applicable across all OWL 2 profiles.
Definition 1 (SROIQ Concepts and Roles). Let NC , NR
and NI be countably infinite and pairwise disjoint sets of respectively
concept names, role names, and individual names, with the top concept ⊤ ∈ NC , the bottom concept ⊥ ∈ NC , and the universal role
𝑈 ∈ NR . An SROIQ role is either a role name or the inverse of a rolename. SROIQ concepts are defined from NC and NI by induction
with the constructs of ¬ (negation), ⊓ (conjunction), ⊔ (disjunction),∃ (existential restriction), ∀ (value restriction), ≥ and ≤ (qualified
number restriction) and Self (self restriction).
The semantics of SROIQ is defined in terms of an interpretation
I = ⟨Δ I , · I ⟩, where Δ I is the domain of the interpretation (a nonempty set), and · I denotes the interpretation function, which assigns
to every individual 𝑎 ∈ NI an element 𝑎 I ∈ Δ I , to every conceptname 𝐴 ∈ NC a set 𝐴 I ⊆ Δ I , and to every role name 𝑟 ∈ NR abinary relation 𝑟 I ⊆ Δ I × Δ I . The interpretation function · I is
inductively extended to other SROIQ concepts as in [2].
Let I be an interpretation. I is a model of an ontology O, written
I |= O, iff every axiom in O is true in I. An axiom 𝛼 is a logicalconsequence of an ontology O, written O |= 𝛼, iff 𝛼 is true in every
model I of O. In this paper, a signature sig ⊆ NC is defined as a setof concept names. Let sig(𝑋 ) denote the set of the concept names
present in 𝑋 , where 𝑋 ranges over concepts, axioms, and sets ofaxioms (ontologies).

2.2

Metadata of OWL Ontologies

Metadata refers to information about the ontology or knowledge
artifact itself, distinct from the domain knowledge it represents.
For instance, if a class like “Electron” is authored by a specific individual, say “Woodstock” on a particular date, this constitutes an
editorial statement about the class rather than its individual instances. Dublin Core1 offers a set of annotations for such metadata,
1 https://www.dublincore.org/

which are accessible within tools like Protégé[21], although they
are not inherent to OWL 2. In OWL ontologies, metadata can be
categorized into three main types:• Editorial/Provenance Meta Statements: These encompass
information about the knowledge acquisition process and its
sources. This includes details about the author, date of entry,
revision history, authority, and more. The Dublin Core subset is a
widely adopted standard for editorial and provenance metadata,with some statements being temporary and geared towards development processes, while others are intended to be permanent.
• Explanatory Statements: These consist of text-based definitions, guidelines, comments, and other explanatory content. They
often incorporate natural language definitions for classes, alongwith comments, evidence, and provenance information related
to the conceptualization of the class.
• Structural Information about the Artefact: Some information
artefacts contain meta-models or structural information that
describes their own organization. For example, regular patternsof axioms may be employed, and templates for these patterns
can be part of the meta-model. This aspect focuses on describing
how the ontology is constructed, rather than the ontology model
itself.
Metadata in OWL ontologies serves multiple purposes, including
documentation, data integration, reasoning, and interoperability. It
enhances the understanding of ontology content, facilitates ontology management, and supports various Semantic Web applications
by providing context and context-awareness for ontology elements.

2.3

Modularization and Uniform Interpolation

Modularization can be defined in various ways depending on theproperties of the computed modules. The definition given in this paper is a generalized one that collects common conditions necessary
for an ontology to be recognized as a module. More specific definitions of modularization can be derived by introducing particularconditions into this generalized framework.
Definition 2 (Module). Let O be an ontology in a DL L andΣ ⊆ sig(O) be a set of concept names (i.e., the seed signature). An
L-ontology M is a Σ-module of O iff the following conditions hold:(1) M ⊆ O, and(2) for any L-axiom 𝛼 with sig(𝛼) ⊆ Σ, M |= 𝛼 iff O |= 𝛼.
The definition of uniform interpolation is given as follows.
Definition 3 (Uniform Interpolant). Let O be an ontology
in a DL L and Σ ⊆ sig(O) be a set of concept names (i.e., the seedsignature). An L-ontology V is a Σ-uniform interpolant of O iff thefollowing conditions hold:(i) sig(V) ⊆ Σ, and(ii) for any L-axiom 𝛼 with sig(𝛼) ⊆ Σ, V |= 𝛼 iff O |= 𝛼.
Σ-modules and Σ-uniform interpolants have exactly the same
logical consequences in the seed signature Σ. The difference is that,while a module is always a syntactic subset of the given ontology,
and may use names outside of Σ, a uniform interpolant uses only
the names in Σ. We therefore call the view computed by uniform
interpolation a signature-restricted abstract. A large number of new
axioms will be deduced from the given ontology in order to preserve the semantics of the Σ-names when eliminating the othernames from the ontology, i.e., the computation of uniform interpolants relies on more reasoning than that of modules. This canlead to uniform interpolants containing substantially more complex
axioms than the input ontology [19]. This is why the problem of
uniform interpolation is generally believed to be computationallyharder than modularization [15]. We regard modularization and uniform interpolation as ‘non-standard” forms of reasoning, because it
cannot be reduced to the “standard” satisfiability/entailment tests.

3

METADATA-BASED TERM SELECTION

Our term selection approach accommodates ontologies described
in OWL 2, which are based on the description logic SROIQ [14];see the Description Logic Handbook [2] for a detailed descriptionof the syntax and semantics of description logics.
Arguably, most topics can be sufficiently summarized or definedby a set of keywords (i.e., key concept names), with less reliance onrole names. Therefore, in this paper, we consider seed signatures
solely as a set of concept names.
Given an ontology O and a seed signature Σ ⊆ sig(O) consistingof either a single or a few concept names, normally suggested bya group of domain experts or simply chosen by users, as the mostrepresentative keywords for the topic of interest, our approach com′putes an extension Σ of Σ through a three-step process involving
concept representation learning, computation of relevance values, and′signature extension based on relevance values. The resulting Σ serves
as the updated seed signature fed into subsequent modularization
and uniform interpolation procedures.

3.1

Concept Representation Learning

Concept representation learning involves the conversion of every
concept name 𝐴 in O into a D-dimensional vector, denoted as e𝐴 ,within a vector space. These vectors are constructed with consideration of the “relevance” of each concept name 𝐴 to the seed signatureΣ and are computed based on important metadata of O.
Our concept representation learning model is based on the coreOWL2Vec* [6], an ontology embedding framework for computing
vector representations of concept names in OWL ontologies as
expressive as SROIQ. OWL2Vec* computes the embedding of an
OWL ontology based on a corpus of token sequences, which are
generated from the ontology’s metadata. This metadata includes
diverse components, encompassing the graph structure of the ontology represented as an RDF graph (a collection of RDF triples)
derived from the OWL ontology through the OWL2Vec* transformation. Additionally, it incorporates what is commonly referred toas the “lexical information” about the ontology, which encompasses
annotations. Furthermore, it encompasses the “logical information”
concerning the concepts and roles within the ontology, encompassing relationships like subsumption, equivalence, and disjointness,among others.
It should be noted that OWL2Vec* was originally designed for
purposes other than term selection tasks. Therefore, we have mademodifications to the core OWL2Vec* model to optimize its performance for downstream term selection tasks. Specifically, we haveintroduced a fine-tuning process specifically tailored to enhance ontology embedding. Further elaboration on this fine-tuning process
can be found in Section 4.

Algorithm 1 Nearest Neighbour Ranking
Input: A set 𝑁𝐶 of concept names, 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 𝐴′ ∈ Σ do
5:𝑔(𝐴) := min (𝑑 (e𝐴 , e𝐴′ ) , 𝑔(𝐴)).
6:
end for
7: end for8: 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

3.2

Computing Relevance Values

This step computes the relevance value of every non-seed conceptname 𝐵 in O to Σ. This computation is based on the relative distance between 𝐵 and its nearest seed neighbor within the vector
space. The relevance value is a scalar within the range of [0, 1],
where a value of 1 indicates the highest level of relevance, whilethat of 0 is the lowest. The computation of this relevance value
is performed using our newly developed algorithm, known as the
Nearest Neighbor Ranking algorithm (NN-RANK), which is shownin Algorithm 1.
More specifically, NN-RANK computes the distance from eachnon-seed name to each seed name in the vector space. In principle,
several distance functions 𝑑 : R𝐷 × R𝐷 → [0, ∞] can be employed
for this purpose. However, in our experiments, the Cosine distance,
formulated as:e𝐴 · e𝐵𝑑 (e𝐴 , e𝐵 ) = 1 −∥e𝐴 ∥ 2 ∥e𝐵 ∥ 2
has proven to be the most effective measure of relevance comparedto euclidean distance and dot product similarity. Based on this formula, |Σ| distance values are computed for each non-seed name 𝐴.
Among these values, the smallest one is identified as the valid distance value of 𝐴 to Σ. NN-RANK subsequently arranges all concept
names in O in ascending order based on their valid distance values.
Concept names with smaller valid distance values are considered
to be semantically more relevant to the seed signature, and consequently, to the central topic. These valid distance values (alongwith the corresponding concept names) are then uniformly mapped
to a range between 0 and 1. The outcome represents the relevancevalue of each 𝐴 with respect to Σ.

3.3

Relevance-Based Seed Signature Extension

A question naturally emerges at this stage: how can the computed
relevance values be effectively employed to guide the selection of
meaningful terms for ontology abstraction? Different application

demands may warrant varying strategies. In the absence of a wellestablished gold standard, a practical approach is to quantify the“degree” of relevance and determine to what extent a concept namecan be considered “relevant” to the seeds in Σ. In this work, we set
a threshold 𝜎 within the range of 0 to 1 to represent the “degree”
of relevance. Our approach extends the primitive seed signature Σ
by including concept names with a relevance value greater than orequal to 𝜎. The result is Σ′ = Σ ∪ {𝐴 | 𝐴 ∈ sig(O) ∧ 𝑓 (𝐴, Σ) ≥ 𝜎 }.
The higher the threshold 𝜎, the smaller the extension obtained.
Computing | sig(O)| × |Σ| distances has a linear time complexity
w.r.t. | sig(O)|, and the subsequent sorting operation has a log-linear
time complexity w.r.t. | sig(O)|.

4EMPIRICAL STUDY OF NN-RANK

In this study, we employed NN-RANK to predict SNOMED CT Refset components. The objective was to demonstrate the algorithm’s
capability to augment a given seed signature Σ with concept namesthat exhibit high relevance to the initial seeds within a vector space.
All evaluations were conducted on a server equipped with an Intel(R) Xeon(R) Gold 5117 CPU @ 2.00GHz and 128 GB of memory.
SNOMED CT2 is currently the most comprehensive, multilingual
clinical healthcare ontology in the world. A SNOMED CT Refset3
constitutes a compilation of SNOMED CT components that sharespecific attributes or characteristics, often related to a particulardomain or field. As an illustrative example, consider the Malaria
Refset, curated by the National Resource Centre for EHR Standards
in India. This Refset includes various findings, disorders, and organisms directly associated with Malaria. Arguably, Refsets officiallypublished by a group of ontology engineers and domain experts
can be regarded as complete and precise standards for abstracting
specific domains within SNOMED CT, such as Malaria.
The task was to predict concepts within SNOMED CT Refsets
based on a seed signature. This seed signature could be either
randomly generated or manually selected from the Refsets. The
task was meticulously designed to align with real-world scenarios
in which we aimed to create new Refsets with minimal involvement from domain experts. We operated under the assumption that
Refsets developed by domain experts represented “complete” and“precise” fragments, containing concepts intricately linked at thesemantic level, often within the same clinical domain. This predictive task of SNOMED CT Refset components served as a crucial
evaluation metric for the performance of term selection models.
To accurately position our algorithm within the landscape ofexisting approaches, we conducted a comparative analysis of NNRANK against two alternative term selection approaches. These
approaches, which we considered as baselines, are as follows:• star-modularization: An approach adapted from locality-based
modularization [12]. It involves considering all concept names
within the computed module as an extension of the seed signature. While not necessarily ideal, this method serves as a means
to expand the seed signature. Under this approach, the relevancevalue 𝑓 (𝐴, Σ) of concept name 𝐴 is assigned a value of 1 if 𝐴 ispresent in the signature of the computed module, and 0 otherwise.

• Sig-Ext (Signature Extension): This approach, based solely on
geographic connections [5], is configured with a specified depth
parameter 𝑑.
Additionally, we also conducted a comparative evaluation of NNRANK against Meta-SVDD [9], a model designed for few-shot oneclass classification problems. Using Meta-SVDD, we extracted patterns from existing Refsets to improve its predictive performance
when applied to new Refset components.
We utilized the International Edition of SNOMED CT (version
July 2020) for our experiments. This edition contains 354,256 concepts, 355,214 logical axioms, and 1,506,185 description axioms. Our
study focused on two sets of publicly accessible and actively usedterm collections, namely the NHS Refsets4 and the NRC Refsets5 . TheNHS Refsets, curated by the National Health Service (NHS) in theUK, provide a subset of components derived from the full SNOMEDCT Edition, specifically tailored to meet specific requirements. The
NRC Refsets, on the other hand, were created and released by the
National Resource Centre for EHR Standards (NRCeS) in India. This
collection comprises 30 distinct Refsets, each focusing on concepts
related to common diseases.
We adopted two established metrics that were widely used inclassification and ranking tasks, namely the Normalized Discounted
Cumulative Gain (NDCG) and Area under the ROC Curve (AUC),
to assess the performance of our term selection models. Both metrics yield higher (lower) values when a model makes more (less)accurate predictions, effectively quantifying the similarity between
the model’s approximations and the Refset components.
The ontology embedding generated by OWL2Vec* for SNOMED
CT was applied to create the concept embeddings, with each concept represented as a 200-dimensional vector. Differing from theoriginal OWL2Vec* model, we implemented a fine-tuning process
tailored for this task to further enhance the ontology embedding.
Specifically, Refsets in this procedure were transformed into documents containing (concept_uri, refset_identifier, concept_uri) triples.
Subsequently, we employed a Word2Vec model to refine the precomputed concept embedding based on these documents. The finetuning process followed a 10-fold cross-validation approach. Thismeans that the evaluations for any Refset were based on a concept
embedding fine-tuned on 90% Refsets other than itself.
For NRC Refsets, we used two distinct seed signatures Σ𝑟 andΣ𝑠 throughout the experiment, each containing 𝐾 concepts. Σ𝑟 was
randomly chosen from the entire pool of the Refset concepts, whileΣ𝑠 was carefully crafted to ensure that the 𝐾 seeds it encompassed
could provide multifaceted coverage of the topic. For NHS Refsets,
we used a separate set of Σ𝑟 generated following the same strategy.
It was imperative to have the flexibility to adjust the size 𝐾 of theinitial seed signature in accordance with the specific application
requirements. In real-world scenarios, the seed signature may be
manually selected, and a smaller value of 𝐾 translates to reduced
manual effort. Consequently, we adopted 𝐾 = 5 in our experiments.
We employed the SyntacticLocalityModuleExtractor class fromthe OWL API6 to generate star-modules. As previously mentioned,

4 https://dd4c.digital.nhs.uk/dd4c/
2 https://www.snomed.org/

5 https://www.nrces.in/resources#snomedct_releases

3 https://confluence.ihtsdotools.org/display/DOCGLOSS/refset

6 https://owlcs.github.io/owlapi/

Methods

NHS Refsets

NRC Refsets

NDCG

Star-modularization
Sig-Ext (d=1)
Sig-Ext (d=2)
Meta-SVDD
NN-RANK
NN-RANK + fine-tuning

AUC

NDCG

AUC

K=1

K=5

K=1

K=5

K=1

K=5

K=1

K=5

40.93 ± 14.61
68.57 ± 20.36
69.50 ± 20.13

47.33 ± 13.36
49.14 ± 10.92
47.99 ± 11.66
67.72 ± 23.26
77.93 ± 14.91
78.76 ± 14.62

50.84 ± 1.10
92.19 ± 11.19
93.33 ± 9.57

54.73 ± 5.56
54.31 ± 5.58
54.31 ± 5.58
91.55 ± 10.43
96.49 ± 5.11
96.98 ± 4.62

49.10 ± 16.23
71.32 ± 14.33
73.57 ± 12.54

51.83 ± 14.62
55.68 ± 11.06
54.31 ± 11.81
71.65 ± 16.62
77.25 ± 10.03
80.19 ± 9.14

50.64 ± 0.98
89.66 ± 8.42
90.40 ± 8.43

54.58 ± 7.82
53.60 ± 6.73
53.78 ± 6.91
88.81 ± 8.87
94.29 ± 5.51
94.79 ± 5.69

Table 1: Results on NHS, NRC Refsets using Σ𝑟 (the higher the better).

Methods

NDCG

Star-modularization
Sig-Ext (d=1)
Sig-Ext (d=2)
Meta-SVDD
NN-RANK
NN-RANK + fine-tuning

AUC

K=1

K=3

K=5

K=1

K=3

K=5

48.85 ± 16.68
49.97 ± 15.36
49.56 ± 15.82
71.28 ± 12.25
79.77 ± 11.79
80.39 ± 12.02

50.65 ± 15.26
53.42 ± 12.16
52.33 ± 13.06
74.91 ± 16.48
83.67 ± 10.74
84.41 ± 10.95

52.25 ± 14.42
55.76 ± 10.48
54.38 ± 11.36
75.24 ± 13.73
84.83 ± 9.95
85.53 ± 10.20

50.82 ± 2.01
50.80 ± 1.53
50.87 ± 1.60
72.4 ± 16.23
94.07 ± 5.11
94.65 ± 5.01

53.21 ± 5.53
52.14 ± 3.89
52.28 ± 4.01
86.83 ± 10.05
96.09 ± 3.73
96.49 ± 3.73

54.68 ± 7.50
53.34 ± 5.81
53.48 ± 5.93
92.01 ± 6.45
96.64 ± 3.09
96.97 ± 3.06

Table 2: Results for NRC Refset using Σ𝑠 (the higher the better).

all concept names contained in the star-modules collectively constitute the extended seed signature. To generate the extended seedsignature using the Sig-Ext method, we utilized the official implementation7 . As for Meta-SVDD, our implementation was developed
based on the source code provided by [7].

4.1

Results and Analysis

The results (mean value ± standard deviation of the two measures)presented in Tables 1 and 2 show that embedding-based methods
outperformed their logical counterparts in the above scenarios. Thisis because, the logical approaches, not being initially designed forthis particular task, omitted the ontology’s lexical information. As
it turned out, this lexical information was of key importance when
it came to evaluating the semantic relevance between concepts.
Furthermore, NN-RANK exhibited a slight performance advantage over Meta-SVDD, especially when taking Σ𝑠 as the seed signature. To provide a more in-depth understanding of the workingsand effectiveness of NN-RANK in this context, we conducted a casestudy using the Malaria Refset mentioned earlier. Figure 2 illustrates the distribution of the Malaria Refset components and other
SNOMED CT concepts in a 2-dimensional vector space. As depictedin the figure, the Refset components exhibited a tendency to form
several smaller clusters, each containing highly semantically relevant concepts. Instead of being a single large cluster, the entire
Refset comprised several concept clusters. This implies that when
two seed concepts 𝐴1 and 𝐴2 were provided, any concept 𝐴 exhibiting similarity to either 𝐴1 or 𝐴2 , quantified by 𝑑 (e𝐴, e𝐴1 ) < 𝜖 or𝑑 (e𝐴, e𝐴2 ) < 𝜖 with 𝜖 representing a small value greater than 0,
had a higher likelihood of being a component of the Refset compared to another concept 𝐴 that resembled the average of e𝐴1
7 http://bit.ly/2JEarazand e𝐴2 , denoted as 𝑑 e𝐴, (e𝐴1 + e𝐴2 )/2 < 𝜖. NN-RANK was
specifically designed to accommodate this multi-cluster patternand demonstrated superior performance compared to other models
that utilized concept embeddings. The performance of NN-RANK
could be significantly enhanced when the seed signatures described
the topic from various perspectives. In the case of a high-quality
primitive seed signature such as Σ𝑠 , increasing the size of the seedsignature typically led to more accurate selection results.

4.2

Time Efficiency

In the current configuration with parameters set to |𝑁𝐶 | = 354, 256,
𝐾 = 5, 𝐷 = 200 and Cosine distance serving as the distance metric, NN-RANK successfully computed Σ′ in just five seconds. In
contrast, alternative approaches such as Star-modularization and
Sig-Ext necessitated a timeframe ranging from several minutes toeven hours for performing similar computations on large-scale ontologies like SNOMED CT. The Meta-SVDD model, in the same
configuration, converged within five minutes. While acknowledging that our approach does incur a more substantial training duration—approximately 4 hours—for generating embedding vectors on
SNOMED CT, this investment in time is deemed justifiable within
practical applications. The rationale behind this is that the training
phase is conducted a single time, yet it has the potential to produce
significant and relevant outcomes across a multitude of applications,extending indefinitely into future applications. Furthermore, it isworth noting that the required training time is subject to adjustment
contingent upon the scale of the ontology, with typical instances
requiring less than one hour when the ontology comprises fewer
than 100,000 logical and annotation axioms. This capability to tailor
the training time according to the ontology’s scale enhances theadaptability and efficiency of our approach.

Figure 3: The ontology abstraction framework

Figure 2: The distribution of components within the malaria
Refset and other SNOMED CT concepts is illustrated in thisfigure, encompassing 170 concepts from the malaria Refset
and 1700 random concepts outside the Refset. Each data pointon the graph represents a SNOMED CT concept, with its color
indicating its relevance to the seed signatures computed by
NN-RANK (deeper colors signifying higher relevance). The
shape of each point distinguishes its type, with a cross denoting Refset components and circles representing concepts
outside the Refset. Seed concepts are denoted by blue stars,
accompanied by corresponding tags. These tags correspondto labels as follows: A - Malaria (disorder), B - Allergy to primaquine (finding), C - Accidental pyrimethamine poisoning(disorder), D - Malaria outbreak education (procedure), E Antimalarial drug adverse reaction (disorder).

5

CASE STUDY: ONTOLOGY ABSTRACTION

In this section, we understand how extending the input signature
with NN-RANK brings distinct advantages for the two ontology
abstraction approaches — modularization and uniform interpolation. To evaluate the effectiveness of our term selection approach,
we required a test ontology with sufficient meaningful metadata.
To this end, we selected HeLiS8 , an ALCH IQ (D) ontology that
describes knowledge related to food and activity from a nutritional
perspective. The experiment was conducted using HeLiS version
1.10, which consisted of 172,213 axioms, 277 concepts, and 50 roles.

5.1

Setup Details

First, we created 10 concept subsets from sig(O𝐻𝑒𝐿𝑖𝑆 ) to serve as
the initial seed signatures, denoted as Σ𝑟 , with set sizes ranging from
1 to 5. As the selection process was random, the chosen concept
8 https://horus-ai.fbk.eu/helis/

names might pertain to different topics encompassed by the Helis
ontology. NN-RANK then computed the extended seed signatures
based on these initial selections.
Given that most real-world applications typically require smaller
ontology abstracts, the size of the seed signature is expected to berelatively small. This correlation arises because the size of generated
ontology abstracts is directly proportional to the size of the input
seed signature. Consequently, we only included concept names fromΣ′ whose relevance values to the original Σ𝑟 fell within the top 10%(i.e., by setting the threshold at 0.9). These selected concept names
were collected into the final seed signature, serving as input to thesubsequent modularization and uniform interpolation procedures.
Figure 3 illustrates the ontology abstraction pipeline employing theterm selection approach.
For our computations, we employed UI-FAME [24] to computeΣ-uniform interpolants and OWL API to compute Σ-star-modules,
as these tools are publicly accessible. Notably, both methods preserved the complete logical consequences of the input signature Σ′
within O𝐻𝑒𝐿𝑖𝑆 [12, 16]. Subsequently, the abstraction results generated by these two tools using the input of Σ′ (denoted as Σ′ +UIFAME, Σ′ +Star-modularization) were evaluated using four metrics:
module size |M|, module inherent richness InhRich, module intra
distance IntraDist, and module cohesion Cohesion. A module characterized by relatively smaller size, higher inherent richness, relatively smaller intra distance, and higher cohesion was consideredmore compact. Additionally, we conducted a comparative analysis
between Σ𝑟 +Star-modularization and Σ′ +Star-modularization.

5.2

Results and Analysis

We conducted a comparison between Σ′ +UI-FAME and Σ′ +Starmodularization to assess the effectiveness of NN-RANK with different abstraction methods. Table 3 provides insights into this comparison, revealing that UI-FAME generated more compact abstractions. Additionally, it was observed that UI-FAME exhibited sensitivity to the input signature. These findings align with expectations
since locality-based modularization introduced additional terms notpresent in Σ′ , whereas uniform interpolation adhered to Σ′ . Further
experiments with thresholds set at 0.3, 0.5, and 0.7 indicated thatthe size of Σ′ did not significantly impact the compactness of thelocality-based module abstraction.

Metrics|M |InhRichIntraDist
Cohesion

K=1

K=5

Star-modularization

UI-FAME

Star-modularization

UI-FAME171 ± 142.92 ± 0.1249683.90 ± 94.61
0.08 ± 0.01

20 ± 72.1 ± 1.25
618.75 ± 617.87
0.19 ± 0.09

174 ± 15
4.08 ± 0.1749798.70 ± 278.77
0.08 ± 0.00

18 ± 83.75 ± 0.49
289.50 ± 344.26
0.15 ± 0.10

Table 3: Module Compactness Evaluation (Using the top 10% of Σ′ as input). |M|: The total number of concepts, roles, andindividuals in M. InhRich: The average number of subclasses per class. IntraDist: The overall distance between the entities in
the module. Cohesion: The degree to which entities are interrelated within the module.)

Term selection plays a crucial role in allowing users to expand
seed signatures in a customizable manner. In the context of uniform interpolation, selecting appropriate terms for a given topic ispivotal since the semantics of the topic heavily relies on the input
terms. We have observed that insufficient input terms for uniform
interpolation can result in very small abstracts, often containing
numerous trivial axioms like 𝐴 ⊑ ⊤ or concept assertion axioms.
NN-RANK+UI-FAME demonstrates a significant ability to generate knowledge highly relevant to the specified topic. For example,
as shown in Table 4, let us consider the topic “SpecialBread”. The
relevant axioms from O𝐻𝑒𝐿𝑖𝑆 were found in O 𝑓 𝑟𝑎𝑔𝑚𝑒𝑛𝑡 . Notably,“SpecialBread” had five individuals, and these individuals had nosuper-classes other than “SpecialBread”. Applying common sense,
we can infer that “OliveBread” can be linked to “OlivesAndOliveProducts”, “SoyBread” to “SoyProducts”, and “MilkBread” to “MilkAndDairyProducts”. These links were absent however in the logicalcomponents of O𝐻𝑒𝐿𝑖𝑆 .
Without NN-RANK’s extension, these concepts, which are highly
relevant to the central topic “SpecialBread”, could not be preservedin Σ𝑟 +Star-modularization or Σ𝑟 +UI-FAME. In contrast, NN-RANK
effectively preserved them in the seed signature based on the lexical proximity of “OlivesAndOliveProducts”, “SoyProducts”, and“MilkAndDairyProducts” to the individuals of “SpecialBread”.
In summary, NN-RANK can serve as an optimization booster for
modularization and uniform interpolation, aiding them in producing more complete abstracts. In addition, Σ′ +uniform interpolation
resulted in more precise abstracts compared to Σ′ +modularization.

6

CONCLUSION AND FUTURE WORK

While modularization and uniform interpolation provide effectivemeans to the abstraction of OWL ontologies, the process of selecting
relevant terms—designated as seed signatures— for these abstraction approaches has often posed a significant challenge, hindering
users from generating more meaningful ontology abstracts. This
paper presents an initial effort to tackle this challenge by extending
the given seed signature with carefully selected new terms, identified through embedding-based analysis of crucial metadata within
an OWL ontology. An evaluation of this approach, conducted on apredication task involving a SNOMED CT Refset, demonstrated that
our method consistently makes accurate selections when comparedto other term selection baselines. Finally, a case study illustrates that
our term selection approach is capable of producing high-quality
modules and uniform interpolants for OWL ontologies.

Σ𝑟{SpecialBread}

Ofragment

SpecialBread ⊑ Bread{SoyBread, OliveBread, MilkBread,
OilBread, RyeBread}⊑ SpecialBreadΣ′ @10SpecialBread
Bread
WhiteBread
PizzaAndFocacciaBread
OlivesAndOliveProducts
SoyProducts
LegumesAndLegumeProducts
WheatFlour
WholeWheatFlour
MilkAndDairyProducts

Table 4: Term seletion for SpecialBread topic in HeLiSThe absence of standardized benchmarks remains a primary challenge when assessing the performance of term selection methods.
Therefore, it would be beneficial to create predefined query answering instances generated from the input ontology. These instances
can help verify the completeness and precision of the generated
abstracts of OWL ontologies. For a problem 𝑄 that can be answeredby querying an ontology O, a satisfactory abstract M of O, given
an input signature Σ, should be capable of answering 𝑄 when 𝑄 isrelevant to Σ. Conversely, it should not be able to answer 𝑄 when
𝑄 is not relevant to Σ.
Furthermore, the quality of term selection results heavily relieson the complexity of the OWL ontology embedding method. One
major limitation of using OWL2Vec* for term selection is its inability to effectively capture logical information. Therefore, our current
focus is on finding ways to map OWL ontologies into vector spaces
with minimal loss of information. It’s important to note that ourcurrent experiments have only considered concepts, but we plan toincorporate roles in future research.

ACKNOWLEDGMENTS
The authors would like to thank the reviewers for their insightfulcomments and good suggestions. This work was supported by the
National Natural Science Foundation of China (grant 62006114), theNatural Science Foundation of Jiangsu Province (grant BK20211150)
and the Xiaomi Foundation.

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