A nonmonotonic extension of KLM Preferential Logic P

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.