In this paper we provide a semantic reconstruction of rational closure. We first consider rational closure as defined by Lehman and Magidor [33] for propositional logic, and we provide a semantic characterization based on a minimal models mechanism on rational models. Then we extend the whole formalism and semantics to Description Logics, by focusing our attention to the standard ALC : we first naturally adapt to Description Logics Lehman and Magidor's propositional rational closure, starting from an extension of ALC with a typicality operator T that selects the most typical instances of a concept C (hence T(C) stands for typical C ). Then, for the Description Logics, we define a minimal model semantics for the logic ALC and we show that it provides a semantic characterization for the rational closure of a Knowledge base. We consider both the rational closure of the TBox and the rational closure of the ABox.

Semantic characterization of Rational Closure: from Propositional Logic to Description Logics

GLIOZZI, Valentina;POZZATO, GIAN LUCA
2015-01-01

Abstract

In this paper we provide a semantic reconstruction of rational closure. We first consider rational closure as defined by Lehman and Magidor [33] for propositional logic, and we provide a semantic characterization based on a minimal models mechanism on rational models. Then we extend the whole formalism and semantics to Description Logics, by focusing our attention to the standard ALC : we first naturally adapt to Description Logics Lehman and Magidor's propositional rational closure, starting from an extension of ALC with a typicality operator T that selects the most typical instances of a concept C (hence T(C) stands for typical C ). Then, for the Description Logics, we define a minimal model semantics for the logic ALC and we show that it provides a semantic characterization for the rational closure of a Knowledge base. We consider both the rational closure of the TBox and the rational closure of the ABox.
2015
226
1
33
rational closure, description logics, nonmonotonic reasoning
Giordano, Laura; Gliozzi, Valentina; Olivetti, Nicola; Pozzato, Gian Luca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1526077
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