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Proof Theory for Functional Modal Logic

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Abstract

We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \(\mathord {\sim }\mathord {\Box }A\equiv \mathord {\Box }\mathord {\sim }A\). We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.

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  1. School of Historical and Philosophical Studies, The University of Melbourne, Parkville, 3010, Australia

    Shawn Standefer

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  1. Shawn Standefer
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Correspondence to Shawn Standefer.

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Standefer, S. Proof Theory for Functional Modal Logic. Stud Logica 106, 49–84 (2018). https://doi.org/10.1007/s11225-017-9725-0

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