Reasoning About Typicality in Description Logics: the Logic ALC + Tmin Laura Giordano⋆ , Valentina Gliozzi⊙ , Nicola Olivetti∗ , Gian Luca Pozzato⊙ Dip. di Informatica - Univ. Piemonte O. “A. Avogadro” - [email protected] Dip. di Informatica - Universit` a di Torino - {gliozzi,pozzato}@di.unito.it LSIS-UMR CNRS 6168 Univ. “P. C´ezanne” - [email protected]

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Abstract In our recent research [2] we have proposed a nonmonotonic extension ALC + Tmin of the Description Logic ALC for reasoning about prototypical properties and inheritance with exception. The logic ALC+Tmin is built upon a previously introduced (monotonic) logic ALC + T [1], that is obtained by adding a typicality operator T to 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 ALC + Tmin for ALC + T. The intuition is that preferred, or minimal models are those that maximise typical instances of concepts. By means of ALC + Tmin we are able to infer defeasible properties of (explicit or implicit) individuals. We are able to provide a decision procedure for checking satisfiability and validity in ALC + Tmin . Our decision procedure has the form of tableaux calculus, with a two-step tableau construction. The idea is that the top level construction generates open branches that are candidates to represent minimal models, whereas the auxiliary construction checks whether a candidate branch represents indeed a minimal model. Our procedure can be used to determine constructively an upper bound of the complexity of ALC +Tmin . Namely we obtain that checking query entailment for ALC + Tmin is in co-NExpNP .

References 1. L. Giordano, V. Gliozzi, N. Olivetti, and G. L. Pozzato. Preferential Description Logics. In LPAR 2007. LNCS(LNAI), vol. 4790, pp. 257-272, 2007. 2. L. Giordano, V. Gliozzi, N. Olivetti, and G. L. Pozzato. Reasoning About Typicality in Preferential Description Logics. In Proc. of JELIA 2008. LNCS(LNAI), vol. 5293, pp. 192-205, 2008.

Reasoning About Typicality in Description Logics: the ...

In our recent research [2] we have proposed a nonmonotonic extension ALC +. Tmin of the Description Logic ALC for reasoning about prototypical properties.
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