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.
A nonmonotonic extension of KLM Preferential Logic P
GLIOZZI, Valentina;POZZATO, GIAN LUCA
2010-01-01
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.
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