Extracting Finite Sets of Entailments from OWL Ontologies

Abstract. The canonical standard description logic reasoning service is classification, that is, the generation of the set of atomic subsumptions which are entailed by some ontology. While this consequence relation is well defined and finite, there is significant variance in the composition of that set. For example, it is common (in tools and in discussion) to exclude some tautologies (e.g., A ⊑ ⊤, A ⊑ A). While for many purposes such divergences are harmless, there are many for which precision about what appears in the classification is essential, for example, estimating differences in logical content. In this paper, we propose definitions for different types of finite entailment sets of an OWL ontology based on the transitive closure and transitive reduction of its asserted and inferred class graphs. The purpose of this work is to introduce a flexible and extensible specification for selecting a particular set of entailments, with the aim of ensuring the correctness and replicability of OWL-based applications.

A Corpus of OWL DL Ontologies.

Abstract. Tool development for and empirical experimentation in OWL ontology engineering require a wide variety of suitable ontologies as input for testing and evaluation purposes. Empirical activities often resort to (somewhat arbitrarily) hand curated corpora available on the web, such as the NCBO BioPortal and the TONES Repository, or manually select a set of well-known ontologies. Results may be biased, even heavily, towards these datasets. Sampling from a large corpus of ontologies, on the other hand, may lead to more representative results. Current large scale repositories/web crawls are mostly uncurated, suffer from duplication and contain large numbers of ontology versions, variants, and facets, and therefore do not lend themselves to random sampling. In this paper, we describe the creation of a corpus of OWL DL ontologies using strategies such as web crawling, various forms of de-duplications and manual cleaning, which allows random sampling of ontologies for a variety of empirical applications

Diversity of Reason: Equivalence Relations over Description Logic Explanations

Abstract. Given the high expressivity of modern ontology languages, such as OWL, there is the possibility for great diversity in the logical content of ontologies. Informally, this can be seen by the constant evolution of reasoners to deal with new sorts of content and the range of optimisations reasoners need in order to be competitive. More formally, the fact that many naturally occurring entailments have multiple justifications (i.e., minimal entailing subsets) indicates that ontologies often overdetermine their consequences, indicating a diversity in supporting reasons. However, the multiplicity of justifications might be due mostly to diverse material, not formal, grounds for an entailment. That is, the logical form of these multiple reasons could be less diverse than their numbers suggest. In the present paper, we introduce and explore several equivalence relations over justifications for entailments of OWL ontologies. These equivalence relations range from strict isomorphism to a looser notions which cover similarities between justifications containing different concept expressions or possibly different numbers of axioms. We survey a corpus of ontologies from the bio-medical domain and find that large numbers of justifications can often be reduced to a significantly smaller set of justifications which are isomorphic with respect to one of the given definitions.

The justificatory structure of OWL ontologies

Abstract. Current ontology development tools offer debugging support by presenting justifications for entailments of OWL ontologies. In many cases even a single entailment may have many distinct justifications, and justifications for distinct entailments may be critically related. We call the set of relations between multiple justifications the justificatory structure of an ontology. A restricted analysis of justificatory structure has already been successfully exploited to reduce effort when debugging ontologies with large numbers of unsatisfiable classes by identifying root unsatisfiable classes. In this paper we present a preliminary analytical framework for the justificatory structure of an ontology and explore possible applications.