  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.
