Abstract
In this paper we propose a nonmonotonic extension 
of the Description Logic \(\mathcal{ALC}\) for reasoning about prototypical properties and inheritance with exception. The logic 
is built upon a previously introduced (monotonic) logic 
, that is obtained by adding a typicality operator T to \(\mathcal{ALC}\). The operator T is intended to select the “most normal” or “most typical” instances of a concept, so that knowledge bases may contain subsumption relations of the form“T(C) is subsumed by P”, expressing that typical C-members have the property P. In order to perform nonmonotonic inferences, we define a “minimal model” semantics 
for 
. The intuition is that preferred, or minimal models are those that maximise typical instances of concepts. By means of 
we are able to infer defeasible properties of (explicit or implicit) individuals. We also present a tableau calculus for deciding 
entailment.
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
Baader, F., Hollunder, B.: Embedding defaults into terminological knowledge representation formalisms. J. Autom. Reasoning 14(1), 149–180 (1995)
Baader, F., Hollunder, B.: Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic. J. of Automated Reasoning (JAR) 15(1), 41–68 (1995)
Bonatti, P.A., Lutz, C., Wolter, F.: Description logics with circumscription. In: Proc. of KR, pp. 400–410 (2006)
Buchheit, M., Donini, F.M., Schaerf, A.: Decidable reasoning in terminological knowledge representation systems. J. Artif. Int. Research (JAIR) 1, 109–138 (1993)
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., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. In: KR 2004, pp. 141–151 (2004)
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)
Giugno, R., Lukasiewicz, T.: P-\(\mathcal{SHOQ}\)(D): A Probabilistic Extension of \(\mathcal{SHOQ}\)(D) for Probabilistic Ontologies in the Semantic Web. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 86–97. Springer, Heidelberg (2002)
Ke, P., Sattler, U.: Next Steps for Description Logics of Minimal Knowledge and Negation as Failure. In: DL 2008 (2008)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1-2), 167–207 (1990)
Moinard, Y.: General Preferential Entailments as Circumscriptions. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 532–543. Springer, Heidelberg (2001)
Straccia, U.: Default inheritance reasoning in hybrid kl-one-style logics. In: Proc. of IJCAI, pp. 676–681 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L. (2008). Reasoning about Typicality in Preferential Description Logics. In: Hölldobler, S., Lutz, C., Wansing, H. (eds) Logics in Artificial Intelligence. JELIA 2008. Lecture Notes in Computer Science(), vol 5293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87803-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-87803-2_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87802-5
Online ISBN: 978-3-540-87803-2
eBook Packages: Computer ScienceComputer Science (R0)