Partial MaxSAT Approach to Nonmonotonic Reasoning with System W

Abstract

The only recently introduced System W is a nonmonotonicinductive inference operator exhibiting some notable proper-ties like extending rational closure and satisfying syntax split-ting postulates for inference from conditional belief bases.A semantic model of system W is given by its underlyingpreferred structure of worlds, a strict partial order on the setof propositional interpretations, also called possible worlds,over the signature of the belief base. Existing implementa-tions of system W are severely limited by the number ofpropositional variables that occur in a belief base becauseof the exponentially growing number of possible worlds. Inthis paper, we present an approach to realizing nonmono-tonic reasoning with system W by using partial maximumsatisfiability (PMaxSAT) problems and exploiting the powerof current PMaxSAT solvers. An evaluation of our approachdemonstrates that it outperforms previous implementations ofsystem W and scales reasoning with system W up to a newdimension.