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On witnessed models in fuzzy logic. II. (English) Zbl 1126.03031
Summary: First the expansion of the Łukasiewicz (propositional and predicated) logic by the unary connectives of dividing by any natural number (rational Łukasiewicz logic) is studied; it is shown that in the predicate case the expansion is conservative w.r.t. witnessed standard 1-tautologies. This result is used to prove that the set of witnessed standard 1-tautologies of the predicate product logic is $$\Pi_{2}$$-hard.
For Part I see ibid. 53, No. 1, 66–77 (2007; Zbl 1110.03013).

MSC:
 03B52 Fuzzy logic; logic of vagueness 03B50 Many-valued logic 03D35 Undecidability and degrees of sets of sentences
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References:
 [1] Gerla, Neural Network World 6 pp 579– (2001) [2] Metamathematics of Fuzzy Logic (Kluwer, 1998). [3] Hájek, Math. Logic Quart. 53 pp 66– (2007) [4] and , Triangular norm based predicate fuzzy logics. To appear in ”Proceedings of Linz Seminar 2005”. [5] Hájek, J. Symbolic Logic 71 pp 863– (2006) [6] Hájek, Fuzzy sets and systems 154 pp 1– (2005)
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