Cathoristic Logic A Logic for Capturing Inferences Between Atomic Sentences

摘要

Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a number of results such as compact- . ness, a semantic characterisation of elementary equivalence, the existence of a quadratic-time decision procedure, and Brandom's incompatibility semantics property. We demonstrate the usefulness of the logic as a language for knowledge representation.