An Investigation of Definability in Ontology Alignment

The ability to rewrite defined ontological entities into syntactically different, but semantically equivalent forms is an important property of Definability. While rewriting has been extensively studied, the practical applicability of currently existing methods is limited, as they are bounded to particular Description Logics (DLs), and they often present only theoretical results. Moreover, these efforts focus on computing single definitions, whereas the ability to find the complete set of alternatives, or even just their signature, can support ontology alignment, and semantic interoperability in general. As the number of possible rewritings is potentially exponential in the size of the ontology, we present a novel approach that provides a comprehensive and efficient way to compute in practice all definition signatures of the feasible (given pre-defined complexity bounds) defined entities described using a DL language for which a particular definability property holds (Beth definability). This paper assesses the prevalence, extent and merits of definability over large and diverse corpora, and lays the basis for its use in ontology alignment.

1. 1.

   In this paper, we assume familiarity with basic notions of Description Logics [1] and the Web Ontology Language [10] (OWL).

2. 2.

   Horridge et al. [12] introduced an efficient approach that computes either a single, or all justifications of an entailment.

3. 3.

   In this paper, we only focus on concept definability, and omit the description of the approach for determining role definability. However, a full description of the algorithm for deciding role definability is available in [8].

4. 4.

   The OWL API provides methods for extracting several types of LBMs.

5. 5.

   Both Algorithms 1, 2 and 3 are used in practice, where the former is better suited for computing an MDS from a DS that is the RHS signatures of an explicit definition, as such signature typically contain either none, or only a few redundant members (i.e. reaching the worst-case scenario of Algorithms 2 and 3).

6. 6.

   Further details on patterns, and the axiom generation algorithm are presented in [8].

7. 7.

   For example, given two versions of an ontology, the one with more defined entities or higher MDS to entity ratio is more valuable, as it may permit the expression of more entities with alignments, that are typically incomplete [7].

8. 8.

   HermiT performs faster with most datasets, however Pellet was able to load and process some ontologies that HermiT could not (due to ontologies using datatypes that are not part of the OWL 2 datatype map and no custom datatype definition was given).

9. 9.

   http://www.csc.liv.ac.uk/~dgeleta/ontodef.html.

10. 10.

    http://owl.cs.manchester.ac.uk/tools/repositories/.

11. 11.

    http://oaei.ontologymatching.org.

12. 12.

    The MDS expansion (Algorithm 5) is restricted to computing an MDS union size \(\mathcal {S} \le 20\). This excluded no entities in the Conference, and 441 in the LargeBio corpus.

13. 13.

    Pattern numbers reference Table 1, Cmb. denotes those MDS cases that do not correspond to any individual pattern, but to a combination of patterns. Patterns that have no MDS in the sample corpus are omitted for brevity.

14. 14.

    An entity e is covered by a mapping c in an alignment \(\mathcal {A}\) iff \(\{ \exists c \in \mathcal {A} | c:\left\langle e, e', r \right\rangle \}\).

15. 15.

    Error #1 and #2 can also be detected without MDSs, via classifying the ontology and inspecting the resulting tree for unsatisfiable or equivalent concepts, respectively.

16. 16.

    \(\mathsf {Anthropometrics}\) means measurement of the size and proportions of the human body. Axioms \(\alpha _2, \alpha _3, \alpha _4\) are correct, as height, weight and BMI are all type of measurements that make up the general class \(\mathsf {Anthropometrics}\), but axiom \(\alpha _1\) is incorrect as height and weight measurements would share nothing in common, i.e. their intersection would be empty. The correct representation would be to describe \(\mathsf {Anthropometrics}\) as a disjoint union of these concepts.

Authors and Affiliations

1. Department of Computer Science, University of Liverpool, Liverpool, UK

   David Geleta, Terry R. Payne & Valentina Tamma

Corresponding author

Correspondence to David Geleta .

Editors and Affiliations

1. Linköping University, Linköping, Sweden

   Eva Blomqvist

2. University of Bologna, Bologna, Italy

   Paolo Ciancarini

3. University of Bologna, Bologna, Italy

   Francesco Poggi

4. University of Bologna, Bologna, Italy

   Fabio Vitali

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