Relevant Agents

March 2010

(with Marta Bílková, Ondrej Majer and Michal Peliš), “Relevant Agents,” pages 22–38, in Advances in Modal Logic, Volume 8, College Publications, 2010.

Majer and Peliš have proposed a relevant logic for epistemic agents, providing a novel extension of the relevant logic R with a distinctive epistemic modality K, which is at the one and the same time factive (Kφ → φ is a theorem) and an existential normal modal operator (K(φ ∨ ψ) → (Kφ ∨ Kψ) is also a theorem). The intended interpretation is that Kφ holds (relative to a situation s) if there is a resource available at s, confirming φ. 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.

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