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On theories and models in fuzzy predicate logics. (English) Zbl 1111.03030
This is a nice contribution to first-order mathematical fuzzy logic. The basic system is the monoidal t-norm logic MTL, i.e., the logic of the left-continuous t-norms. This well-known system is treated here in an a bit more general form, which allows the authors to subsume a whole family of further logics to these considerations, mainly extensions of MTL. All these logics have algebraic semantics.
First, the authors give a slight generalization of the completeness theorem, mainly saying that models with degree sets without unnecassary degrees suffice. Then they study conservative extensions of elementary theories via different forms of Henkin extensions. And they give a syntactic characterization of witnessed models. Finally they transfer most of these results to extensions which contain also the $$\triangle$$-operator.

##### MSC:
 03B52 Fuzzy logic; logic of vagueness 03B50 Many-valued logic 03C07 Basic properties of first-order languages and structures
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