Abstract
We extend the Description Logic \(\mathcal{ALC}\) with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called \(\mathcal{ALC}+{\bf T}\). The typicality operator is intended to select the “most normal” or “most typical” instances of a concept. In our framework, knowledge bases may then contain, in addition to ordinary ABoxes and TBoxes, subsumption relations of the form “T(C) is subsumed by P”, expressing that typical C-members have the property P. The semantics of a typicality operator is defined by a set of postulates that are strongly related to Kraus-Lehmann-Magidor axioms of preferential logic P. We first show that T enjoys a simple semantics provided by ordinary structures equipped by a preference relation. This allows us to obtain a modal interpretation of the typicality operator. Using such a modal interpretation, we present a tableau calculus for deciding satisfiability of \(\mathcal{ALC}+{\bf T}\) knowledge bases. Our calculus gives a nondeterministic-exponential time decision procedure for satisfiability of \(\mathcal{ALC}+{\bf T}\). We then extend \(\mathcal{ALC}+{\bf T}\) knowledge bases by a nonmonotonic completion that allows inferring defeasible properties of specific concept instances.
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Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L. (2007). Preferential Description Logics. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_20
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DOI: https://doi.org/10.1007/978-3-540-75560-9_20
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