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  1. Arithmetical Complexity of Fuzzy Predicate Logics—a Survey II.Petr Hájek - 2009 - Annals of Pure and Applied Logic 161 (2):212-219.
    Results on arithmetical complexity of important sets of formulas of several fuzzy predicate logics are surveyed and some new results are proven.
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  • Formal Systems of Fuzzy Logic and Their Fragments.Petr Cintula, Petr Hájek & Rostislav Horčík - 2007 - Annals of Pure and Applied Logic 150 (1):40-65.
    Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of theorems with much wider (...)
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  • Franco Montagna’s Work on Provability Logic and Many-Valued Logic.Lev Beklemishev & Tommaso Flaminio - 2016 - Studia Logica 104 (1):1-46.
    Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic.
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  • Distinguished Algebraic Semantics for T -Norm Based Fuzzy Logics: Methods and Algebraic Equivalencies.Petr Cintula, Francesc Esteva, Joan Gispert, Lluís Godo, Franco Montagna & Carles Noguera - 2009 - Annals of Pure and Applied Logic 160 (1):53-81.
    This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...)
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  • A Henkin-Style Proof of Completeness for First-Order Algebraizable Logics.Petr Cintula & Carles Noguera - 2015 - Journal of Symbolic Logic 80 (1):341-358.
  • On Witnessed Models in Fuzzy Logic.Petr Hájek - 2007 - Mathematical Logic Quarterly 53 (1):66-77.
    Witnessed models of fuzzy predicate logic are models in which each quantified formula is witnessed, i.e. the truth value of a universally quantified formula is the minimum of the values of its instances and similarly for existential quantification. Systematic theory of known fuzzy logics endowed with this semantics is developed with special attention paid to problems of arithmetical complexity of sets of tautologies and of satisfiable formulas.
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