Relevant agents

Majer and Peliš proposed a relevant logic for epistemic agents, providing a novel extension of the relevant logic $\mathsf{R}$ with a distinctive epistemic modality $K$, which is at the one and the same time factive ($K\varphi\to\varphi$ is a theorem) and an existential normal modal operator $(K(\varphi\vee\psi)\to(K\varphi\vee K\psi)$ is also a theorem). The intended interpretation is that $K\varphi$ holds (relative to a situation $s$) if there is a resource available at $s$, confirming $\varphi$. In this article we expand the class of models to the broader class of ‘general epistemic frames’. With this generalisation we provide a sound and complete axiomatisation for the logic of general relevant epistemic frames. We also show, that each of the modal axioms characterises some natural subclasses of general frames.