Archive for Mathematical Logic 44 (1):97-114 (2004)

.Given a class C of t-norm BL-algebras, one may wonder which is the complexity of the set Taut of predicate formulas which are valid in any algebra in C. We first characterize the classes C for which Taut is recursively axiomatizable, and we show that this is the case iff C only consists of the Gödel algebra on [0,1]. We then prove that in all cases except from a finite number Taut is not even arithmetical. Finally we consider predicate monadic logics TautM of classes C of t-norm BL-algebras, and we prove that they are undecidable.
Keywords Predicate many-valued logics  T-norm semantics  Complexity
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Reprint years 2005
DOI 10.1007/s00153-004-0231-5
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References found in this work BETA

Fuzzy Logic and Arithmetical Hierarchy III.Petr Hájek - 2001 - Studia Logica 68 (1):129-142.
Monadic Fuzzy Predicate Logics.Petr Hájek - 2002 - Studia Logica 71 (2):165-175.

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Formal Systems of Fuzzy Logic and Their Fragments.Petr Cintula, Petr Hájek & Rostislav Horčík - 2007 - Annals of Pure and Applied Logic 150 (1):40-65.
On Witnessed Models in Fuzzy Logic.Petr Hájek - 2007 - Mathematical Logic Quarterly 53 (1):66-77.
Mathematical Fuzzy Logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.

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