This paper provides a general semantic framework for nonmonotonic reasoning, based on a minimal models semantics on the top of KLMsystems 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 characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they are allowed to vary. In both cases a knowledge base must be expanded with a suitable set of consistency assumptions, represented by negated conditionals. The correspondence between rational closure and minimal model semantics suggests the possibility of defining variants of rational closure by changing either the underlying modal logic or the comparison relation on models.

A minimal model semantics for rational closure

GLIOZZI, Valentina;POZZATO, GIAN LUCA
2012

Abstract

This paper provides a general semantic framework for nonmonotonic reasoning, based on a minimal models semantics on the top of KLMsystems 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 characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they are allowed to vary. In both cases a knowledge base must be expanded with a suitable set of consistency assumptions, represented by negated conditionals. The correspondence between rational closure and minimal model semantics suggests the possibility of defining variants of rational closure by changing either the underlying modal logic or the comparison relation on models.
NMR 2012: 14th International Workshop on Non-Monotonic Reasoning
Roma, Italy
June 2012
Proceedings of NMR 2012: 14th International Workshop on Non-Monotonic Reasoning
Riccardo Rosati, Stefan Woltran
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http://www.dbai.tuwien.ac.at/NMR12/
Description Logics; Nonmonotonic reasoning
Laura Giordano; Valentina Gliozzi; Nicola Olivetti; Gian Luca Pozzato
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/147333
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