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Contraction-Free Linear Depth Sequent Calculi for Intuitionistic Propositional Logic with the Subformula Property and Minimal Depth Counter-Models

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Abstract

In this paper we present LSJ, a contraction-free sequent calculus for Intuitionistic propositional logic whose proofs are linearly bounded in the length of the formula to be proved and satisfy the subformula property. We also introduce a sequent calculus RJ for intuitionistic unprovability with the same properties of LSJ. We show that from a refutation of RJ of a sequent σ we can extract a Kripke counter-model for σ. Finally, we provide a procedure that given a sequent σ returns either a proof of σ in LSJ or a refutation in RJ such that the extracted counter-model is of minimal depth.

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Authors and Affiliations

  1. Dipartimento di Informatica e Comunicazione, Università degli Studi dell’Insubria, Via Mazzini 5, 21100, Varese, Italy

    Mauro Ferrari

  2. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, Via Comelico 39, 20135, Milano, Italy

    Camillo Fiorentini

  3. Dipartimento di Metodi Quantitativi per le Scienze Economiche Aziendali, Università degli Studi di Milano-Bicocca, P.zza dell’Ateneo Nuovo 1, 20126, Milano, Italy

    Guido Fiorino

Authors
  1. Mauro Ferrari
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  2. Camillo Fiorentini
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  3. Guido Fiorino
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Correspondence to Camillo Fiorentini.

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Ferrari, M., Fiorentini, C. & Fiorino, G. Contraction-Free Linear Depth Sequent Calculi for Intuitionistic Propositional Logic with the Subformula Property and Minimal Depth Counter-Models. J Autom Reasoning 51, 129–149 (2013). https://doi.org/10.1007/s10817-012-9252-7

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  • DOI: https://doi.org/10.1007/s10817-012-9252-7

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