A Terminating Evaluation-Driven Variant of G3i

  • Mauro Ferrari
  • Camillo Fiorentini
  • Guido Fiorino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8123)


We present Gbu, a terminating variant of the sequent calculus G3i for intuitionistic propositional logic. Gbu modifies G3i by annotating the sequents so to distinguish rule applications into two phases: an unblocked phase where any rule can be backward applied, and a blocked phase where only right rules can be used. Derivations of Gbu have a trivial translation into G3i. Rules for right implication exploit an evaluation relation, defined on sequents; this is the key tool to avoid the generation of branches of infinite length in proof-search. To prove the completeness of Gbu, we introduce a refutation calculus Rbu for unprovability dual to Gbu. We provide a proof-search procedure that, given a sequent as input, returns either a Rbu-derivation or a Gbu-derivation of it.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mauro Ferrari
    • 1
  • Camillo Fiorentini
    • 2
  • Guido Fiorino
    • 3
  1. 1.DiSTAUniv. degli Studi dell’InsubriaVareseItaly
  2. 2.DIUniv. degli Studi di MilanoMilanoItaly
  3. 3.DISCOUniv. degli Studi di Milano-BicoccaMilanoItaly

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