Cathoristic logic: A modal logic of incompatible propositions

TL;DR

Cathoristic logic introduces a novel modal logic framework that replaces negation with an operator for expressing incompatibility, providing a new tool for knowledge representation with efficient decision procedures.

Contribution

The paper presents the syntax, semantics, proof rules, and key properties of cathoristic logic, a new logic for incompatible propositions, including decision procedures and semantic characterizations.

Findings

Complete proof rules established

Decidable in quadratic time

Supports semantic characterization of elementary equivalence

Abstract

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 compactness, 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.