# Cathoristic Logic

A Logic for Capturing Inferences Between Atomic Sentences

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## 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.

## Keywords

Modal logic Hennessy-Milner logic Transition systems Negation Exclusion Elementary equivalence Incompatibility semantics Knowledge representation Philosophy of language## Notes

### Acknowledgements

We thank Tom Smith, Giacomo Turbanti and the anonymous reviewers for their thoughtful comments.

## Supplementary material

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