Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
Horridge et al. [12] introduced an efficient approach that computes either a single, or all justifications of an entailment.
- 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.
The OWL API provides methods for extracting several types of LBMs.
- 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.
Further details on patterns, and the axiom generation algorithm are presented in [8].
- 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.
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.
- 10.
- 11.
- 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.
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.
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.
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.
\(\mathsf {Anthropometrics}\) 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.
References
Baader, F.: The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)
Beth, E.W.: On Padoa’s method in the theory of definition. Indag. Math. 15, 330–339 (1953)
Cheatham, M., Dragisic, Z., Euzenat, J., Faria, D., Ferrara, A., Flouris, G., Fundulaki, I., Granada, R., Ivanova, V., Jiménez-Ruiz, E., Lambrix, P., Montanelli, S., Pesquita, C., Saveta, T., Shvaiko, P., Solimando, A., dos Santos, C.T., Zamazal, O.: Results of the ontology alignment evaluation initiative 2015. In: Proceedings of the 10th International Workshop on Ontology Matching, pp. 60–115 (2015)
David, J., Euzenat, J., Šváb-Zamazal, O.: Ontology similarity in the alignment space. In: Patel-Schneider, P.F., Pan, Y., Hitzler, P., Mika, P., Zhang, L., Pan, J.Z., Horrocks, I., Glimm, B. (eds.) ISWC 2010, Part I. LNCS, vol. 6496, pp. 129–144. Springer, Heidelberg (2010)
Del Vescovo, C., Klinov, P., Parsia, B., Sattler, U., Schneider, T., Tsarkov, D.: Empirical study of logic-based modules: cheap is cheerful. In: Alani, H., et al. (eds.) ISWC 2013, Part I. LNCS, vol. 8218, pp. 84–100. Springer, Heidelberg (2013)
Donnelly, K.: SNOMED-CT: the advanced terminology and coding system for eHealth. Stud. Health Technol. Inform. 121, 279 (2006)
Euzenat, J., Shvaiko, P.: Ontology Matching, 2nd edn. Springer, Heidelberg (2013)
Geleta, D., Payne, T.R., Tamma, V.: Computing minimal definition signatures in description logic ontologies. Technical report, University of Liverpool (2016). https://intranet.csc.liv.ac.uk/research/techreports/tr2016/ulcs-16-003.pdf
Glimm, B., Horrocks, I., Motik, B., Stoilos, G., Wang, Z.: HermiT: an OWL 2 reasoner. J. Autom. Reason. 53(3), 245–269 (2014)
Grau, B.C., Horrocks, I., Motik, B., Parsia, B., Patel-Schneider, P., Sattler, U.: OWL 2: the next step for OWL. Web Semant. 6(4), 309–322 (2008)
Hoogland, E., et al.: Definability and interpolation: Model-Theoretic Investigations. Institute for Logic, Language and Computation, Amsterdam (2001)
Horridge, M.: Justification based explanation in ontologies. Ph.D. thesis, University of Manchester (2011)
Horridge, M., Bechhofer, S.: The OWL API: a Java API for OWL ontologies. Semant. Web 2(1), 11–21 (2011)
Matentzoglu, N., Bail, S., Parsia, B.: A snapshot of the OWL web. In: Alani, H., et al. (eds.) ISWC 2013, Part I. LNCS, vol. 8218, pp. 331–346. Springer, Heidelberg (2013)
Rosse, C., Mejino Jr., J.L.: The foundational model of anatomy ontology. In: Burger, A., Davidson, D., Baldock, R. (eds.) Anatomy Ontologies for Bioinformatics. Computational Biology, vol. 6, pp. 59–117. Springer, Heidelberg (2008)
Sattler, U., Schneider, T., Zakharyaschev, M.: Which kind of module should I extract? Descr. Log. 477, 78 (2009)
Scharffe, F., Zamazal, O., Fensel, D.: Ontology alignment design patterns. Knowl. Inf. Syst. 40(1), 1–28 (2014)
Seylan, I., Franconi, E., De Bruijn, J.: Effective query rewriting with ontologies over DBoxes. In: IJCAI, vol. 9, pp. 923–929. Citeseer (2009)
Sirin, E., Parsia, B., Grau, B.C., Kalyanpur, A., Katz, Y.: Pellet: a practical OWL-DL reasoner. Web Semant.: Sci. Serv. Agents World Wide Web 5(2), 51–53 (2007)
Stuckenschmidt, H., Predoiu, L., Meilicke, C.: Learning complex ontology alignments a challenge for ILP research. In: Proceedings of the 18th International Conference on Inductive Logic Programming (2008)
Ten Cate, B., Franconi, E., Seylan, I.: Beth definability in expressive description logics. J. Artif. Intell. Res. (JAIR) 48, 347–414 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Geleta, D., Payne, T.R., Tamma, V. (2016). An Investigation of Definability in Ontology Alignment. In: Blomqvist, E., Ciancarini, P., Poggi, F., Vitali, F. (eds) Knowledge Engineering and Knowledge Management. EKAW 2016. Lecture Notes in Computer Science(), vol 10024. Springer, Cham. https://doi.org/10.1007/978-3-319-49004-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-49004-5_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49003-8
Online ISBN: 978-3-319-49004-5
eBook Packages: Computer ScienceComputer Science (R0)