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Fuzzy logic and arithmetical hierarchy. IV. (English) Zbl 1084.03020
Hendricks, Vincent (ed.) et al., First-order logic revisited. Proceedings of the conference FOL75 – 75 years of first-order logic, Humboldt-University, Berlin, Germany, September 18–21, 2003. Berlin: Logos Verlag (ISBN 3-8325-0475-3/pbk). Logische Philosophie 12, 107-115 (2004).
The author, in previous papers of this sequence [see Zbl 0857.03011, Zbl 0869.03015 and Zbl 0988.03042] as well as F. Montagna [Stud. Log. 68, 143–152 (2001; Zbl 0985.03014)] have given a series of complexity results for first-order t-norm based fuzzy logics, for the cases that these basic t-norms are the Łukasiewicz, the Gödel, or the product t-norm.
Here the author extends these results to t-norms that have as first summands in their ordinal sum representation isomorphic copies of the Gödel or the Łukasiewicz t-norm, and in the latter case also to the first-order logics which additionally have the Baaz \(\Delta\)-operator.
For the entire collection see [Zbl 1076.03004].

03B52 Fuzzy logic; logic of vagueness
03B50 Many-valued logic
03D15 Complexity of computation (including implicit computational complexity)