Relevant epistemic logic with state-sensitive topics

We present a sound and complete axiomatisation of the epistemic logic C.RC. In the logic, the propositional fragment is Classical, while agents’ epistemic attitudes are closed under on–topic relevant consequence, as modeled by Relevant Containment logic. By doing so, C.RC complies with a principle of minimal mutilation of classical logic and lifts some limitations of existing frameworks, such as (i) logics of analytic implication, (ii) topic-sensitive analyses of epistemic modals, and (iii) the logic of relevant reasoners in classical worlds.