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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Tableau Calculus for Basic Fuzzy Logic BL
verfasst von : Agnieszka Kułlacka
Erschienen in: Information Processing and Management of Uncertainty in Knowledge-Based Systems
Verlag: Springer International Publishing
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In this paper we present a tableau calculus for BL, basic fuzzy logic introduced by Petr Hájek in his monograph
Metamathematics of Fuzzy Logic
. We show that it is sound and complete with respect to continuous t-norms, and demonstrate the refutational procedure and the search for models procedure on a selected example. The idea of the calculus is based on the decomposition theorem for a continuous t-norm, by which this operation is shown to be equivalent to the ordinal sum of a family of t-norms defined on countably many intervals.