BDD-Based Automated Reasoning for Propositional Bi-Intuitionistic Tense Logics

  • Rajeev Goré
  • Jimmy Thomson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)

Abstract

We give Binary Decision Diagram (BDD) based methods for deciding validity and satisfiability of propositional Intuitionistic Logic  Int and Bi-intuitionistic Tense Logic BiKt. We handle intuitionistic implication and bi-intuitionistic exclusion by treating them as modalities, but the move to an intuitionistic basis requires careful analysis for handling the reflexivity, transitivity and antisymmetry of the underlying Kripke relation. BiKt requires a further extension to handle the interactions between the intuitionistic and modal binary relations, and their converses. We explain our methodology for using the Kripke semantics of these logics to constrain the underlying least and greatest fixpoint approaches of the finite model construction. With some optimisations this technique is competitive with the state of the art theorem provers for Intuitionistic Logic using the ILTP benchmark and randomly generated formulae.

Keywords

Modal Logic Binary Relation Theorem Prover Inverse Method Intuitionistic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Rajeev Goré
    • 1
  • Jimmy Thomson
    • 1
  1. 1.Logic and Computation Group, Research School of Computer ScienceThe Australian National UniversityAustralia

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