Journal of Automated Reasoning

, Volume 51, Issue 2, pp 129–149 | Cite as

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



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.


Intuitionistic propositional logic Sequent calculi Subformula property Decision procedures Counter-models generation 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Mauro Ferrari
    • 1
  • Camillo Fiorentini
    • 2
  • Guido Fiorino
    • 3
  1. 1.Dipartimento di Informatica e ComunicazioneUniversità degli Studi dell’InsubriaVareseItaly
  2. 2.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly
  3. 3.Dipartimento di Metodi Quantitativi per le Scienze Economiche AziendaliUniversità degli Studi di Milano-BicoccaMilanoItaly

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