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

Studia Logica 71 (2):227-245 (2002)
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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1016500922708
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Sándor Jenei (2009). On the Reflection Invariance of Residuated Chains. Annals of Pure and Applied Logic 161 (2):220-227.

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