The representation of an entity in an ontology may require complex expressions to capture all of its relevant characteristics. If an entity can be defined based on its characteristics, then its definition can be explicitly stated in most knowledge representation languages, such as the Web Ontology Language (OWL). Specifically, a domain-specific entity can be identified by a name in an ontology, which can be declared to be logically equivalent to a more complex expression This not only fixes the meaning of the entity in the ontology but also allows its name to replace the more complex expression throughout the ontology. Consistently using concise and informative names for domain-specific entities in an ontology can arguably enhance ontology comprehension, maintenance, and usability in practice. This raises the question of the extent to which entities represented in ontologies are associated with concrete names and how such names are used. In this paper, we analyze how often named classes in OWL ontologies are defined as logically equivalent to complex expressions. We investigate whether such named classes are consistently used whenever possible and whether they are associated with labels intended for human understanding. Our ifndings indicate that complex class expressions are frequently declared to be equivalent to named classes in ontologies, and that such named classes are linked to human readable labels. While there seems to be a tendency to encourage the reuse of these names, we also observe a notable number of instances where such named classes are not consistently reused despite being defined.
The representation of an entity in an ontology typically involves statements about the entity’s
characteristics. When an entity can be defined based on its characteristics, the definition may
include an informative name by which the entity can be referred to. Specifically, an entity’s
name may be used instead of its more complex definitional description. Despite the potential
benefits of consistently using concise and informative names whenever possible, it has been
observed that this practice is not always followed in published ontologies. To illustrate this, we
revisit a concrete example taken from the Galen ontology, which was originally presented by
Nikitina and Koopmann [
actsSpecificallyOn.(Blood
⊓ ∃ hasPhysicalState.(PhysicalState ⊓ ∃ hasState.Liquid)) ⊓ ∃ hasOutcome.SolidBlood
This axiom is arguably complex due to both its size and the nesting of expressions. However, Galen also contains the following axioms:
Given these equivalences, the named concept LiquidBlood can be used to simplify the representation of Clotting to
actsSpecificallyOn.LiquidBlood ⊓ ∃ hasOutcome.SolidBlood
The latter representation of Clotting is arguably easier to read, comprehend, and maintain. This observation raises questions about the frequency of defining concrete names for complex expressions, the consistency of using such names throughout an ontology, and to what extent the use of names simplifies the definition of more complex concepts. The contributions presented in this paper are as follows: (i) we propose an approach for identifying named classes with logical definitions in ontologies, (ii) we develop techniques for quantifying the use and lack of reuse of such named classes, and (iii) we use these techniques to conduct an empirical investigation on a large and complex corpus of ontologies in the biomedical domain to shed light on the use of such names in real-world ontologies.
We assume the reader to be familiar with OWL [
The Oxford English Dictionary defines the word abbreviation to denote “[t]he result of shortening
something; an abbreviated or condensed form, esp. of a text; a summary, an abridgement” [
(hasTopping some (PizzaTopping and (hasSpiciness some Hot))) 2 = SpicyTopping EquivalentTo PizzaTopping and (hasSpiciness some Hot) 3 = SpicyTopping EquivalentTo HotTopping 4 = DiavolaPizza SubClassOf SpicyPizza 5 = DiavolaPizza SubClassOf Pizza and hasCountryOfOrigin value Italy 6 = NapoletanaPizza SubClassOf Pizza and hasCountryOfOrigin value Italy abbreviation for C in an ontology , if |= EquivalentClasses (A, C). We will refer to the EquivalentClasses axiom as the definition of the abbreviation A.
A complex OWL expression can be equivalent to more than just one named class. We refer to equivalent named classes as synonyms.1 In particular, a synonym for a named class N in an ontology is a named class S s.t. |= EquivalentClasses (S, N) and we will refer to the EquivalentClasses axiom as the synonym’s definition. Please note that synonyms are not necessarily abbreviations. However, a synonym for an abbreviation is also an abbreviation (due to transitivity of EquivalentClasses ).
Both abbreviations and synonyms are notions based on entailment, i.e., an EquivalentClasses axiom with exactly two arguments. However, OWL specifies EquivalentClasses as an -ary constructor. So, for the purpose of analyzing how abbreviations and synonyms are specified in ontologies, we introduce the notion syntactic definitions types for both abbreviations and synonyms. In particular, an axiom of the form EquivalentClasses (A, C) and EquivalentClasses (S, A) will be referred to as simple definitions for the abbreviation A and the synonym S respectively. An axiom of the form EquivalentClasses (A, C1, . . . , C) where C1, . . . C are complex class expressions is a ambiguous definition of A. An axiom of the form EquivalentClasses (S1, . . . , S) is an enumerative definition for the synonyms S1, . . . , S. And lastly, an axiom of the form EquivalentClasses (S1, . . . , S, C1, . . . , C) will be referred to as a compound definition for S1, . . . , S, which are both synonyms and abbreviations.
With this notion of definition types, we can quantify how abbreviations and synonyms are
specified explicitly in an ontology. However, counting implicit definitions of abbreviations
and synonyms is not as straightforward, as extracting nfiite sets of entailments is a non-trivial
matter [
Consider the example ontology shown in Figure 1. Here, the abbreviation SpicyPizza is
specified via a simple definition in axiom 1 and occurs on the right-hand side of 4. So, we say
an abbreviation is used if it occurs in an OWL axiom that is not its definition. In addition to
the use of an abbreviation, we can also determine if an abbreviation is not used even though its
use would be possible. We refer to such a case as an abbreviation’s possible use. For example,
1The Oxford English Dictionary defines the word synonym to denote “Strictly, a word having the same sense as
another (in the same language); [. . .]” [
With the notions of an abbreviation’s use and possible use, we can quantify the impact of abbreviations in an ontology. Before we do so, we come back to the topic of determining both explicit and implicit definitions of abbreviation and synonyms in an ontology.
Explicit definitions for abbreviations can be easily determined by checking the syntactic shape of all axioms in a given ontology. Similarly, implicit definitions can be determined by checking |= EquivalentClasses (A, C) for all pairs of named classes and complex classes occurring in an ontology. However, this becomes impractical for large ontologies with numerous named and complex classes.
Instead, to determine implicit abbreviations, we build upon highly optimized implementations
of the standard reasoning service classification , i.e., computing all entailed SubClassOf and
EquivalentClasses axioms between named classes in an ontology [
More formally, for a given ontology , we create the abbreviation ontology
= ∪ {EquivalentClasses (A, C) | C occurs in , A does not occur in } and compute ICH(). Since the ICH captures all SubClassOf and EquivalentClasses relationships between named classes in an ontology, it is straightforward to identify all named classes in that are equivalent to a newly introduced abbreviation A in .
We will demonstrate this procedure by way of example. Consider the ontology shown in Figure 1. This ontology contains complex class expressions C1, . . . , C6 as shown in Figure 2a. Classifying the abbreviation ontology and inspecting the ICH (see Figure 2) reveals that, for example, SpicyTopping is equivalent to A2, which in turn is equivalent to C2 by construction. So, SpicyTopping is an abbreviation for C2 in .
Before we investigate to what extent abbreviations and synonyms are defined, used, and not used even though this would be possible, we first establish a baseline. This baseline aims to determine whether named classes in ontologies are associated with concrete domain-specific terms that are intended for human interpretation. Specifically, we assess the association of named classes in ontologies with human-readable annotations specified via rdfs:label2 and obo:definition.3 Similarly, we establish a baseline for human-readable synonyms specified 2https://www.w3.org/TR/rdf-schema/#ch_label 3http://purl.obolibrary.org/obo/IAO_0000115 C1 = hasSpiciness some Hot C2 = PizzaTopping and (hasSpiciness some Hot) C3 = hasTopping some (PizzaTopping and (hasSpiciness some Hot)) C4 = Pizza and (hasTopping some (PizzaTopping and (hasSpiciness some Hot))) C5 = hasCountryOfOrigin value Italy C6 = Pizza and hasCountryOfOrigin value Italy (a) Complex class expressions in .
⊤ Hot
A3
Pizza
A5
PizzaTopping
A1 SpicyPizza, A4
A6
HotTopping, SpicyTopping, A2 DiavolaPizza
NapoletanaPizza (b) Visualisation of ICH() without ⊥. via skos:altLabel,4 oio:hasExactSynonym, oio:hasNarrowSynonym, oio:hasBroadSynonym, oio:hasRelatedSynonym,5 or obo:alternativeLabel.6
We conduct our empirical investigation using ontologies indexed in BioPortal as of February
2023.7 The data set is created folllowing the same approach as described by Matentzoglu and
Parsia [
We group ontologies into three disjoint categories. First, ontologies that consist of atomic axioms only, i.e., SubClassOf and EquivalentClasses axioms that have only named classes as arguments. Second, ontologies expressible in ℰ ℒ++, and third, ontologies not expressible in ℰ ℒ++. We refer to these three kinds of ontologies as atomic, ℰ ℒ++, and rich ontologies 4https://www.w3.org/2012/09/odrl/semantic/draft/doco/skos_altLabel.html 5https://raw.githubusercontent.com/geneontology/go-ontology/master/contrib/oboInOwl#{hasExactSynonym, hasNarrowSynonym, hasBroadSynonym, hasRelatedSynonym}. 6http://purl.obolibrary.org/obo/IAO_0000118 7https://bioportal.bioontology.org/
respectively. The study corpus contains 91 atomic ontologies, 88 ℰ ℒ++ ontologies, and 565 rich ontologies. We order ontologies within a category by the size of their TBoxes and assign each ontology an index in ascending order starting with atomic ontologies, then ℰ ℒ++ ontologies, and finally rich ontologies. Figure 3 illustrates this indexing by showing a comparison between the size of an ontology’s (a) TBox and (b) the subset of class expression axioms.
Using the reasoner Konclude (v0.7.0-1138), we successfully classified 714 ontologies (for the purpose of determining implicit synonyms) and 656 abbreviation ontologies (for the purpose of determining implicit abbreviations).
Before presenting our results on abbreviations and synonyms (see Section 3) we report on the use of annotation properties for specifying human-readable labels, definitions, and synonyms. Table 1 illustrates the number of ontologies that ofer human-readable annotations for varying percentages of named classes.
We find that rdfs:labels are available in many ontologies for large proportions of named classes. For instance, 51 + 51 + 232 = 334 ontologies provide rdfs:labels for all named classes. An additional 19 + 16 + 130 = 165 ontologies provide rdfs:labels for at least 90% of named classes (but not 100%), so that (334 + 165)/744 ≈ 67% of ontologies provide rdfs:labels for at least 90% of named classes. This provides strong evidence of the importance of human-readable rdfs:labels for named classes representing domain-specific concepts in biomedical ontologies.
We also find that obo:definitions are used in many ontologies. For example, 226 ontologies, i.e., 226/744 ≈ 30%, provide obo:definitions for at least half of all named classes. While these proportions are smaller compared to rdfs:labels, they are non-trivial and provide evidence that obo:definitions play an important role in many biomedical ontologies.
However, human-readable annotations for synonyms appear to be less common in biomedical ontologies compared to rdfs:labels and obo:definitions. While there are a few ontologies 1 × 106 sm100000 o ixA 10000 fo 1000 reb 100 um 10 N 1
100 200 300 400 500 600 700
that annotate more than 90% of named classes with synonyms, e.g., 12 in the case of skos:alt, a lot of ontologies do not provide such synonym annotations for named classes at all (see last row in Table 1). This suggests that although annotations for synonyms are used in some biomedical ontologies, they do not seem to hold the same level of importance as rdfs:labels and obo:definitions for the most part.
The last observation can also be made w.r.t. the logical notions of abbreviations and synonyms. Figure 4 shows how many EquivalentClassesAxioms are syntactic definition types for abbreviations or synonyms (see Section 3 for definition types). It becomes evident that there are about twice as many ontologies in which abbreviations are (explicitly) defined compared with ontologies in which synonyms are (explicitly) defined — namely 309 and 136 respectively. We also note that abbreviations and synonyms are specified only via simple definitions.
The diference between abbreviations and synonyms is not only evident in the number of ontologies in which they are defined but also in the number of definitions within ontologies. We find that the definitions for abbreviations are more numerous compared to definitions for synonyms. Specifically, there are 105 ontologies that define more than a hundred abbreviations, whereas only eight ontologies have more than a hundred definitions for synonyms. Given these observations, we will focus on abbreviations rather than synonyms in the remainder of this paper and will start with a discussion of explicitly defined abbreviations and then proceed with implicitly defined ones.
(a) Explicitly defined abbreviations.
(b) Implicitly defined abbreviations.
Logical equivalent rewritings for ontologies are usually motivated for the purpose of improved
reasoning performance [
In the work presented in this paper, the focus is not on rewritings that are minimal in size. Rather, we study to what extent domain-specific vocabulary defined in an ontology can be reused to simplify otherwise complex expressions. The main argument being that a meaningful
name is more readily understood by domain experts compared to more complex expressions in OWL. It is important to note that the associated reduction in size is secondary in this context.
The task of determining abbreviations in an ontology (cf. Section 4) can be interpreted as
concept definability, i.e., the problem of finding a definition for a concept name in an ontology [
The OBO Foundry considers naming conventions important for ontology comprehension,
readability, navigability, alignment, and integration [
The use of human-readable names is important, because technical terms in a domain-specific vocabulary tend to be defined in terms of already defined terms. For example, a ’blood assay datum’ is defined as ’A data item that is the specified output of a blood assay’. This definition only makes sense if the notion of a ’blood assay’ is already defined. So, if textual definitions make use of already defined terms, and textual definitions should match logical definitions, as the OBO Foundry advocates, then possible uses of explicitly defined abbreviations (cf. Section 3) should not occur.8
However, our results suggest that even though the reuse of already defined concepts seems to be preferred, there is a non-trivial number of cases in which a complex class expression could be replaced by an existing equivalent named class. It would be interesting to consult with the ontology developers in such cases to determine whether such cases are intended or not. Likewise, it would be interesting to find out whether classes with implicit logical definitions are intentional and should be made explicit, and whether they should be reused whenever possible.
In addition to the question of when to use an abbreviation, is the question of when to introduce a new abbreviation. In particular, if a complex class expression occurs often in an ontology, one may want to think about whether such an expression can be given a meaningful name and which should be used instead.
However, it needs to be highlighted that the introduction of an abbreviation, as defined in this work, changes the meaning of an ontology. Consider the ontology and = ∪ { } where = EquivalentClasses (A, C) is a definition for an abbreviation A. If A does not occur in , then ̸≡ because |= but ̸|= . This change in meaning can be avoided by encoding abbreviations using a meta-language, e.g., OTTR [19], on top of OWL. As an example, consider the ontology = {
Napoletana Diavola Hawaiian
SubClassOf Pizza and hasCountryOfOrigin value Italy, SubClassOf Pizza and hasCountryOfOrigin value Italy,
SubClassOf Pizza and hasCountryOfOrigin value Canada
defined, so that can be encoded as = {
Napoletana Diavola Hawaiian
SubClassOf ItalianPizza, SubClassOf ItalianPizza,
SubClassOf Pizza and hasCountryOfOrigin value Canada Note that ItalianPizza is not an OWL class but an expression in OTTR. In particular, the ontology is semantically equivalent to because the OTTR expression ItalianPizza is indistinguishable from Pizza and hasCountryOfOrigin value Italy on the level of OWL. The use of a meta-level language also opens up possibilities to capture definitions on higher level of abstraction than OWL. In the case of the example ontology , the representation of a pizza’s country of origin could be captured by a parameterized OTTR expression
in can be encoded in a uniform manner giving rise to the following even more meaningful definitions: }. }. = {
Napoletana Diavola Hawaiian
SubClassOf PizzaWithOrigin(Italy), SubClassOf PizzaWithOrigin(Italy), SubClassOf PizzaWithOrigin(Canada) }.
In this paper, we proposed an approach for analyzing and quantifying the use of logical abbreviations, i.e., named classes that are defined to be logically equivalent to complex class expressions. We used this approach to survey biomedical ontologies indexed in BioPortal and find that abbreviations are highly prevalent. Although there are some exceptions, explicitly defined abbreviations tend to be used whenever possible. However, implicitly defined abbreviations often come with many possible uses which rasies the question of whether this is intentional or undesireable. data principles to evaluate ontologies, Database J. Biol. Databases Curation 2021 (2021). URL: https://doi.org/10.1093/database/baab069. doi:10.1093/database/baab069. [19] M. G. Skjaeveland, D. P. Lupp, L. H. Karlsen, H. Forssell, Practical Ontology Pattern Instantiation, Discovery, and Maintenance with Reasonable Ontology Templates, in: ISWC (1), volume 11136 of Lecture Notes in Computer Science, Springer, 2018, pp. 477–494.