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The eighth International ñonference "Advances in Modal Logic" (AiML 2010)
August 27, 2010 16:15, Moscow

Relevant agents

Marta Bílková, Ondrej Majer, Michal Peliš, Greg Restall
 Video records: Windows Media 176.2 Mb Flash Video 336.2 Mb MP4 336.2 Mb

Abstract: 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.