Gian Luca Pozzato

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We define the notion of rational closure in the context of Description Logics. We start from an extension of ALC with a typicality operator T allowing to express concepts of the form T(C), whose meaning is to select the “most normal” instances of a concept C. The semantics we consider is based on rational models and exploits a minimal models mechanism based(More)
We extend the Description Logic ALC with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC + 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(More)
We extend the Description Logic ALC with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC +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(More)
In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics. The calculus uses labels and transition formulas and can be used to prove decidability and space complexity bounds for the respective logics. We also show that these calculi can be the base for uniform proof systems. Moreover, we present CondLean, a(More)
This paper provides a general semantic framework for nonmonotonic reasoning, based on a minimal models semantics on the top of KLM systems for nonmonotonic reasoning. This general framework can be instantiated in order to provide a semantic reconstruction within modal logic of the notion of rational closure, introduced by Lehmann and Magidor. We give two(More)
We present tableau calculi for the logics of nonmonotonic reasoning defined by Kraus, Lehmann and Magidor (KLM). We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative, and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision(More)
In this work we include cardinality restrictions and degrees of expectedness of inclusions in preferential Description Logics. We enrich the language of the nonmonotonic Description Logic DL-LitecT, obtained by adding a typicality operator T to standard DL-Litecore , by allowing inclusions of the form T(C) vd D, where d is a degree of expectedness. We then(More)