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)


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.


Classical Logic Intuitionistic Logic Natural Deduction Sequent Calculus Proof Procedure 
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 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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