Proof analysis in intermediate logics

Archive for Mathematical Logic 51 (1-2):71-92 (2012)

Authors
Sara Negri
University of Helsinki
Abstract
Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the explanation of the rules
Keywords Sequent calculus  Modal logic  Intermediate logic  Labelled deduction  Modal companion
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DOI 10.1007/s00153-011-0254-7
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References found in this work BETA

Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
Structural Proof Theory.Harold T. Hodes - 2006 - Philosophical Review 115 (2):255-258.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.

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Citations of this work BETA

Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
Proof Analysis for Lewis Counterfactuals.Sara Negri & Giorgio Sbardolini - 2016 - Review of Symbolic Logic 9 (1):44-75.

View all 16 citations / Add more citations

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