Analytic Tableaux Calculi for KLM Logics of Nonmonotonic Reasoning

Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca Pozzato

Abstract: We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.