Symmetry and Completeness in Relevant Epistemic Logic

In this paper, we provide an axiom system for the relevant logic of equivalence relation frames and prove completeness for it. This provides a partial answer to the longstanding open problem of axiomatizing frames for relevant modal logics where the modal accessibility relation is symmetric. Following this, we show that the logic enjoys Halldén completeness and that a related logic enjoys the disjunction property. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.