Abstract
We describe ongoing research to support the construction of terminologies with Description Logics. For the explanation of subsumption we search for particular concepts because of their syntactic and semantic properties. More precisely, the set of explanations for a subsumption \(P\sqsubseteq N\) is the set of optimal interpolants for P and N. We provide definitions for optimal interpolation and an algorithm based on Boolean minimisation of concept-names in a tableau proof for \(\mathcal{ALC}\)-satisfiability. Finally, we describe our implementation and some experiments to assess the computational scalability of our proposal.
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References
Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Cambridge University Press, Cambridge (2003)
Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69, 5–40 (2001)
Beckert, B., Goré, R.: Modleantap and modleantest.pl (1998), http://i12www.ira.uka.de/modlean
Borgida, A., Franconi, E., Horrocks, I., McGuinness, D., Patel-Schneider, P.: Explaining \(\mathcal {ALC}\) subsumption. In: DL 1999, pp. 37–40 (1999)
Craig, W.: Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. Journal of Symbolic Logic 22, 269–285 (1957)
Minutes of the DL Implementation Group Workshop, http://dl.kr.org/dig/minutes-012002.html , visited on January 9, 2003
Endriss, U.: Reasoning in description logics with wellington 1. 0. In: Proceedings of the Automated Reasoning Workshop 2000, London, UK (2000)
Kracht, M.: Tools and Techniques in Modal Logic. North-Holland, Amsterdam (1999)
Nebel, B.: Terminological reasoning is inherently intractable. AI 43, 235–249 (1990)
Quine, W.V.: The problem of simplifying truth functions. American Math. Monthly 59, 521–531 (1952)
Rautenberg, W.: Modal tableau calculi and interpolation. Journal of Philosophical Logic 12, 403–423 (1983)
Schlobach, S.: Knowledge Acquisition in Hybrid Knowledge Representation Systems. PhD thesis, University of London (2002)
Schlobach, S.: Optimal interpolation. Technical Report PP-2003-23, Universiteit van Amsterdam, ILLC, Beta Preprint Publication (2003)
Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Proceedings of the eighteenth International Joint Conference on Artificial Intelligence, IJCAI 2003, Morgan Kaufmann, San Francisco (2003)
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Schlobach, S. (2004). Explaining Subsumption by Optimal Interpolation. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_35
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DOI: https://doi.org/10.1007/978-3-540-30227-8_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23242-1
Online ISBN: 978-3-540-30227-8
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