Abstract
We revisit non-monotonic description logics based on circumscription (with preferences) and prove several decidability results for their satisfiability problem. In particular, we consider circumscribed description logics without the finite model property (DL-Lite\(_{\mathcal{F}}\) and \(\mathcal{ALCFI}\)) and with fixed roles (DL-Lite\(_{\mathcal{F}}\) and a fragment of DL-Lite\(_{\mathcal{R}}\)), improving upon previous decidability results that are limited to logics which have the finite model property and do not allow to fix roles during minimization.
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
Preview
Unable to display preview. Download preview PDF.
References
Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-lite family and relations. J. Artif. Intell. Res (JAIR) 36, 1–69 (2009)
Baader, F., Hollunder, B.: Embedding defaults into terminological knowledge representation formalisms. J. Autom. Reasoning 14(1), 149–180 (1995)
Baader, F., McGuiness, D.L., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook: Theory, implementation and applications. Cambridge University Press (2003)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press (2001)
Bonatti, P.A., Faella, M., Sauro, L.: Defeasible inclusions in low-complexity DLs. J. Artif. Intell. Res (JAIR) 42, 719–764 (2011)
Bonatti, P.A., Lutz, C., Wolter, F.: The complexity of circumscription in DLs. J. Artif. Intell. Res (JAIR) 35, 717–773 (2009)
Brewka, G.: The logic of inheritance in frame systems. In: Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI 1987), pp. 483–488. Morgan Kaufmann (1987)
Cadoli, M., Donini, F., Schaerf, M.: Closed world reasoning in hybrid systems. In: Proc. of ISMIS 1990, pp. 474–481. Elsevier (1990)
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Proc. of AAAI 2005, pp. 602–607 (2005)
Casini, G., Straccia, U.: Defeasible inheritance-based description logics. J. Artif. Intell. Res (JAIR) 48, 415–473 (2013)
Donini, F.M., Nardi, D., Rosati, R.: Description logics of minimal knowledge and negation as failure. ACM Trans. Comput. Log. 3(2), 177–225 (2002)
Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. Artificial Intelligence 172(12), 1495–1539 (2008)
Feferman, S., Vaught, R.L.: The first-order properties of algebraic systems. Fundamenta Mathematicae 47, 57–103 (1959)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Preferential description logics. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 257–272. Springer, Heidelberg (2007)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: A non-monotonic description logic for reasoning about typicality. Artif. Intell. 195, 165–202 (2013)
Gottlob, G., Hernich, A., Kupke, C., Lukasiewicz, T.: Equality-friendly well-founded semantics and applications to description logics. In: Description Logics (2012)
Gottlob, G., Hernich, A., Kupke, C., Lukasiewicz, T.: Stable model semantics for guarded existential rules and description logics. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fourteenth International Conference, KR 2014, Vienna, Austria, July 20-24 (2014)
Konev, B., Lutz, C., Walther, D., Wolter, F.: Model-theoretic inseparability and modularity of description logic ontologies. Artif. Intell. 203, 66–103 (2013)
Kontchakov, R., Wolter, F., Zakharyaschev, M.: Logic-based ontology comparison and module extraction, with an application to dl-lite. Artif. Intell. 174(15), 1093–1141 (2010)
Motik, B., Rosati, R.: Reconciling description logics and rules. Journal of the ACM (JACM)Â 57(5), 30 (2010)
Rector, A.L.: Defaults, context, and knowledge: Alternatives for OWL-indexed knowledge bases. In: Pacific Symposium on Biocomputing, pp. 226–237. World Scientific (2004)
Sengupta, K., Krisnadhi, A.A., Hitzler, P.: Local closed world semantics: Grounded circumscription for OWL. In: Aroyo, L., Welty, C., Alani, H., Taylor, J., Bernstein, A., Kagal, L., Noy, N., Blomqvist, E. (eds.) ISWC 2011, Part I. LNCS, vol. 7031, pp. 617–632. Springer, Heidelberg (2011)
Stevens, R., Aranguren, M.E., Wolstencroft, K., Sattler, U., Drummond, N., Horridge, M., Rector, A.L.: Using OWL to model biological knowledge. International Journal of Man-Machine Studies 65(7), 583–594 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bonatti, P., Faella, M., Lutz, C., Sauro, L., Wolter, F. (2015). Decidability of Circumscribed Description Logics Revisited. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. Lecture Notes in Computer Science(), vol 9060. Springer, Cham. https://doi.org/10.1007/978-3-319-14726-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-14726-0_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-14725-3
Online ISBN: 978-3-319-14726-0
eBook Packages: Computer ScienceComputer Science (R0)