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Goal-Directed Proof Search in Multiple-Conclusioned Intuitionistic Logic

  • James Harland
  • Tatjana Lutovac
  • Michael Winikoff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1861)

Abstract

A key property in the definition of logic programming languages is the completeness of goal-directed proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (single-conclusioned) sequent calculus LJ, but has subsequently been adapted to multiple-conclusioned systems such as those for linear logic. Given these developments, it seems interesting to investigate the notion of goal-directed proofs for a multiple-conclusioned sequent calculus for intuitionistic logic, in that this is a logic for which there are both single-conclusioned and multiple-conclusioned systems (although the latter are less well known). In this paper we show that the language obtained for the multiple-conclusioned system differs from that for the single-conclusioned case, show how hereditary Harrop formulae can be recovered, and investigate contraction-free fragments of the logic.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • James Harland
    • 1
  • Tatjana Lutovac
    • 1
  • Michael Winikoff
    • 1
  1. 1.Department of Computer ScienceRoyal Melbourne Institute of TechnologyMelbourneAustralia

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