Studia Logica

, Volume 71, Issue 2, pp 227–245 | Cite as

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

  • Franco Montagna
  • Hiroakira Ono


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.

many-valued logics logics without contraction Kripke semantics left-continuous t-norms 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Franco Montagna
    • 1
  • Hiroakira Ono
    • 2
  1. 1.Department of MathematicsUniversity of SienaSienaItaly
  2. 2.Japan Advanced Institute of Science and TechnologyTatsunokuchi, IshikawaJapan

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