A nonmonotonic extension of KLM preferential logic P

Authors:
Laura Giordano;Valentina Gliozzi;Nicola Olivetti;Gian Luca Pozzato
Affiliations:
Dip. di Informatica, U. Piemonte O., Alessandria, Italy;Dip. Informatica, Univ. di Torino, Italy;LSIS, UMR, CNRS, Marseille, France;Dip. Informatica, Univ. di Torino, Italy
Venue:
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Year:
2010

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Abstract

In this paper, we propose the logic Pmin, which is a nonmonotonic extension of Preferential logic P defined by Kraus, Lehmann and Magidor (KLM). In order to perform nonmonotonic inferences, we define a "minimal model" semantics. Given a modal interpretation of a minimal A-world as A ∧ □¬A, the intuition is that preferred, or minimal models are those that minimize the number of worlds where ¬□¬A holds, that is of A-worlds which are not minimal. We also present a tableau calculus for deciding entailment in Pmin.