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Journal of Logic and Computation

Volume 13, Issue 2, April 2003: pp. 241-259

A Tableau Calculus for Hájek's Logic BL

Franco Montagna1, G. Michele Pinna1 and Elisa B. P. Tiezzi1

1Dipartimento di Matematica, Via del Capitano 15, 53100 Siena, Italy. E-mail: {montagna,pinna,tiezzie}@unisi.it

We introduce a tableau calculus for Háajek's Basic Logic BL. This calculus has many of the desirable properties of a proof system: it is cut-free, it has the subformula property, correctness of proof can be checked in P-time, and the number of symbols in any branch of the reduction tree of any sequent [Ggr] is polynomial in the number of symbols of [Ggr]. As a corollary we obtain an alternative proof of Co-NP completeness of BL.

Keywords: Fuzzy logics; tableau calculus; proof systems

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