Proof Theory for Functional Modal Logic


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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Standefer, S. Proof Theory for Functional Modal Logic. Stud Logica 106, 49–84 (2018).

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  • Functional modal logic
  • Hypersequents
  • Revision theory
  • Proof theory