Proof Theory for Functional Modal Logic

Studia Logica 106 (1):49-84 (2018)

Authors
Shawn Standefer
University of Melbourne
Abstract
We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. 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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DOI 10.1007/s11225-017-9725-0
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References found in this work BETA

Two Notions of Necessity.Martin Davies & Lloyd Humberstone - 1980 - Philosophical Studies 38 (1):1-31.
Conditionals in Theories of Truth.Anil Gupta & Shawn Standefer - 2017 - Journal of Philosophical Logic 46 (1):27-63.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
Contractions of Noncontractive Consequence Relations.Rohan French & David Ripley - 2015 - Review of Symbolic Logic 8 (3):506-528.
A Cut-Free Sequent System for Two-Dimensional Modal Logic, and Why It Matters.Greg Restall - 2012 - Annals of Pure and Applied Logic 163 (11):1611-1623.

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Citations of this work BETA

Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.

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