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Journal of Logic and Computation 2003 13(2):241-259; doi:10.1093/logcom/13.2.241
© 2003 by Oxford University Press
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Original Article

A Tableau Calculus for Hájek's Logic BL

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

1 Dipartimento di Matematica, Via del Capitano 15, 53100 Siena, Italy. E-mail: montagna{at}unisi.itpinna{at}unisi.ittiezzie{at}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 {Gamma} is polynomial in the number of symbols of {Gamma}. As a corollary we obtain an alternative proof of Co-NP completeness of BL.

Keywords: Fuzzy logics; tableau calculus; proof systems

Received 26 March 2001.


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