On the intuitionistic force of classical search (Extended abstract)

  • Eike Ritter
  • David Pym
  • Lincoln Wallen
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1071)

Abstract

The combinatorics of proof-search in classical propositional logic lies at the heart of most efficient proof procedures because the logic admits least-commitment search. The key to extending such methods to quantifiers and non-classical connectives is the problem of recovering this least-commitment principle in the context of the non-classical/non-propositional logic; i.e., characterizing when a least-commitment (classical) search yields sufficient evidence for provability in the (non-classical) logic.

In this paper, we present such a characterization for the (⊃, ∧)-fragment of intuitionistic logic using the λμ-calculus: a system of realizers for classical free deduction (cf. natural deduction) due to Parigot.

We show how this characterization can be used to define a notion of uniform proof, and a corresponding proof procedure, which extends that of Miller et al. to multiple-conclusioned sequent systems. The procedure is sound and complete for the fragment of intuitionistic logic considered and enjoys the combinatorial advantages of search in classical logic.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Eike Ritter
    • 1
  • David Pym
    • 2
  • Lincoln Wallen
    • 3
  1. 1.School of Computer ScienceUniversity of BirminghamUK
  2. 2.Queen Mary & Westfield CollegeUniversity of LondonUK
  3. 3.Computing LaboratoryOxford UniversityUK

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