Efficient Intuitionistic Theorem Proving with the Polarized Inverse Method

  • Sean McLaughlin
  • Frank Pfenning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)


The inverse method is a generic proof search procedure applicable to non-classical logics satisfying cut elimination and the subformula property. In this paper we describe a general architecture and several high-level optimizations that enable its efficient implementation. Some of these rely on logic-specific properties, such as polarization and focusing, which have been shown to hold in a wide range of non-classical logics. Others, such as rule subsumption and recursive backward subsumption apply in general. We empirically evaluate our techniques on first-order intuitionistic logic with our implementation Imogen and demonstrate a substantial improvement over all other existing intuitionistic theorem provers on problems from the ILTP problem library.


Inference Rule Inverse Method Inversion Phase Atomic Formula Intuitionistic Logic 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sean McLaughlin
    • 1
  • Frank Pfenning
    • 1
  1. 1.Department of Computer ScienceCarnegie Mellon UniversityUSA

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