Studia Logica

, Volume 106, Issue 1, pp 49–84

# Proof Theory for Functional Modal Logic

• Shawn Standefer
Article

## 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.

## Keywords

Functional modal logic Hypersequents Revision theory Proof theory

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