A Labelled System for IPL with Variable Splitting

  • Roger Antonsen
  • Arild Waaler
Conference paper

DOI: 10.1007/978-3-540-73595-3_10

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4603)
Cite this paper as:
Antonsen R., Waaler A. (2007) A Labelled System for IPL with Variable Splitting. In: Pfenning F. (eds) Automated Deduction – CADE-21. CADE 2007. Lecture Notes in Computer Science, vol 4603. Springer, Berlin, Heidelberg

Abstract

The paper introduces a free variable, labelled proof system for intuitionistic propositional logic with variable splitting. In this system proofs can be found without backtracking over rules by generating a single, uniform derivation. We prove soundness, introduce a construction that extracts finite countermodels from unprovable sequents, and formulate a branchwise termination condition. This is the first proof system for intuitionistic propositional logic that admits goal-directed search procedures without compromising proof lengths, compared to corresponding tableau calculi.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Roger Antonsen
    • 1
  • Arild Waaler
    • 1
  1. 1.Department of Informatics, University of OsloNorway

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