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Proof-Search and Countermodel Generation in Propositional BI Logic

Extended Abstract
  • Didier Galmiche
  • Daniel Méry
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2215)

Abstract

In this paper, we study proof-search in the propositional BI logic that can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. With its underlying sharing interpretation, BI has been recently used for logic programming or reasoning about mutable data structures. We propose a labelled tableau calculus for BI, the use of labels making it possible to generate countermodels. We show that, from a given formula A, a non-redundant tableau construction procedure terminates and yields either a tableau proof of A or a countermodel of A in terms of the Kripke resource monoid semantics. Moreover, we show the finite model property for BI with respect to this semantics.

Keywords

Induction Hypothesis Logic Programming Intuitionistic Logic Linear Logic Substructural 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 2001

Authors and Affiliations

  • Didier Galmiche
    • 1
  • Daniel Méry
    • 1
  1. 1.LORIA — Université Henri Poincaré, Campus ScientifiqueVandoeuvre-lès-NancyFrance

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