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Complexity of t-tautologies. (English) Zbl 1006.03022
The paper focuses on propositional fuzzy logics based on continuous triangular norms (t-norms). After a brief overview of some principal results in the theory of t-norms, the proof of the main theorem is provided: The set of all t-tautologies (i.e. tautologies w.r.t. arbitrary continuous t-norm) is coNP-complete. From this, it also follows that the universal first-order theory of t-algebras (i.e. algebras \(\langle[0, 1], \star, \rightarrow, 0, 1\rangle\) where \(\star\) is a continuous t-norm and \(\rightarrow\) is its residuum) is coNP-complete.

MSC:
03B52 Fuzzy logic; logic of vagueness
03B25 Decidability of theories and sets of sentences
03D15 Complexity of computation (including implicit computational complexity)
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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