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.
CITATION STYLE
Galmiche, D., & Méry, D. (2001). Proof-search and countermodel generation in propositional BI logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2215, pp. 263–282). Springer Verlag. https://doi.org/10.1007/3-540-45500-0_13
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