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