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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)

Abstract

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.

Keywords

Inference Rule Inverse Method Inversion Phase Atomic Formula 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 2009

Authors and Affiliations

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

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