Analytic Cut-Free Tableaux for Regular Modal Logics of Agent Beliefs

We present a sound and complete tableau calculus for a class $\mathcal{BR}eg$ of extended regular modal logics which contains useful epistemic logics for reasoning about agent beliefs. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. Applying sound global caching to the calculus, we obtain the first optimal (EXPTime) tableau decision procedure for $\mathcal{BR}eg$. We demonstrate the usefulness of $\mathcal{BR}eg$ logics and our tableau calculus using the wise men puzzle and its modified version, which requires axiom (5) for single agents.

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