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Cathoristic Logic: A Modal Logic of Incompatible Propositions

### Richard Evans

Natural language is full of incompatible alternatives. If
Pierre is the current king of France, then nobody else can
simultaneously fill that role. A traffic light can be green,
amber or red - but it cannot be more than one colour at a
time. Mutual exclusion is a natural and ubiquitous
concept. First-order logic can represent mutually exclusive
alternatives, but incompatibility is a 'derived' concept,
expressed using a combination of universal quantification and
identity.

In this talk I will introduce an alternative approach,
Cathoristic logic, where exclusion is expressed directly, as a
first-class concept. Cathoristic logic is a multi-modal logic
containing a new logical primitive allowing the expression of
incompatible sentences. I will present the syntax and
semantics of the logic, and outline 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. I
will demonstrate the usefulness of the logic as a language for
knowledge representation.

Joint work with Martin Berger