A proof-theoretic investigation of a logic of positions

Annals of Pure and Applied Logic 123 (1-3):135-162 (2003)

Abstract
We introduce an extension of natural deduction that is suitable for dealing with modal operators and induction. We provide a proof reduction system and we prove a strong normalization theorem for an intuitionistic calculus. As a consequence we obtain a purely syntactic proof of consistency. We also present a classical calculus and we relate provability in the two calculi by means of an adequate formula translation
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DOI 10.1016/s0168-0072(03)00021-6
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References found in this work BETA

Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
On an Intuitionistic Modal Logic.G. M. Bierman & V. C. V. de Paiva - 2000 - Studia Logica 65 (3):383-416.
Sequent-Systems for Modal Logic.Kosta Došen - 1985 - Journal of Symbolic Logic 50 (1):149-168.
2-Sequent Calculus: A Proof Theory of Modalities.Andrea Masini - 1992 - Annals of Pure and Applied Logic 58 (3):229-246.

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Citations of this work BETA

An Approach to Infinitary Temporal Proof Theory.Stefano Baratella & Andrea Masini - 2004 - Archive for Mathematical Logic 43 (8):965-990.
A Natural Deduction System for Bundled Branching Time Logic.Stefano Baratella & Andrea Masini - 2013 - Journal of Applied Non-Classical Logics 23 (3):268 - 283.
Strong Normalization of Program-Indexed Lambda Calculus.Norihiro Kamide - 2010 - Bulletin of the Section of Logic 39 (1/2):65-78.
Temporal Gödel-Gentzen and Girard Translations.Norihiro Kamide - 2013 - Mathematical Logic Quarterly 59 (1-2):66-83.

View all 6 citations / Add more citations

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