Kripke semantics, undecidability and standard completeness for Esteva and Godo's logic MTL∀

Studia Logica 71 (2):227-245 (2002)
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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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Hiroakira Ono
Japan Advanced Institute of Science and Technology