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Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo's Logic MTL∀

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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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Montagna, F., Ono, H. Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo's Logic MTL∀. Studia Logica 71, 227–245 (2002). https://doi.org/10.1023/A:1016500922708

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