Algebras for Relevant Reasoners

Abstract

The informational interpretations of relevant logic suggest that it provides a natural framework for the development of epistemic logic. This paper proposes a simple extension of relevant modal logic to formalise reasoning about relevant reasoners situated in classical worlds. This approach avoids many of the technical challenges of previous proposals and allows for straightforward algebraic generalisation. The main technical result is a representation theorem for a class of relevant algebras, which provides a solid foundation for further exploration of relevant epistemic logic.