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Communication Dans Un Congrès Année : 2001

Proof-search and countermodel generation in propositional BI Logic - extended abstract -

Didier Galmiche
Daniel Méry

Résumé

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.
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inria-00100565 , version 1 (26-09-2006)

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  • HAL Id : inria-00100565 , version 1

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Didier Galmiche, Daniel Méry. Proof-search and countermodel generation in propositional BI Logic - extended abstract -. 4th International Symposium on Theoretical Aspects of Computer Software - TACS 2001, 2001, Sendai, Japan, pp.263-282. ⟨inria-00100565⟩
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