Abstract
The present paper deals with the predicate version MTL∀ of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono's Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL∀ and classical predicate logic is undecidable. Finally, we prove that MTL∀ is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order.
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