Sequent calculi for propositional nonmonotonic logics

Abstract

A uniform proof-theoretic reconstruction of the major nonmonotonic logics is introduced. It consists of analytic sequent calculi where the details of nonmonotonic assumption making are modelled by an axiomatic rejection method. Another distinctive feature of the calculi is the use of provability constraints that make reasoning largely independent of any specific derivation strategy. The resulting account of nonmonotonic inference is simple and flexible enough to be a promising playground for investigating and comparing proof strategies, and for describing the behavior of automated reasoning systems. We provide some preliminary evidence for this claim by introducing optimized calculi, and by simulating an existing tableaux-based method for circumscription. The calculi for skeptical reasoning support concise proofs that may depend on a strict subset of the given theory. This is a difficult task, given the nonmonotonic behavior of the logics.