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

1 TYPES - Logic, proof Theory and Programming
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
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Document type :
Conference papers
Domain :

https://hal.inria.fr/inria-00100565
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 2:47:38 PM
Last modification on : Monday, February 7, 2022 - 10:04:06 AM

### Identifiers

• HAL Id : inria-00100565, version 1

### Citation

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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