Annals of Pure and Applied Logic 172 (3):102916 (2021)

Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of metalogical properties such as compactness, abstract completeness, the Löwenheim–Skolem property, the Tarski union property, and the Robinson property, among others. As necessary technical restrictions, we assume that the models are valued on finite MTL-chains and the language has a constant for each truth-value.
Keywords Mathematical fuzzy logic  Lindström theorem  Abstract model theory  Many-valued predicate logics
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DOI 10.1016/j.apal.2020.102916
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References found in this work BETA

Model Theory.C. C. Chang & H. Jerome Keisler - 1992 - Studia Logica 51 (1):154-155.
Axioms for Abstract Model Theory.K. Jon Barwise - 1974 - Annals of Mathematical Logic 7 (2-3):221-265.
Omitting Uncountable Types and the Strength of [0,1]-Valued Logics.Xavier Caicedo & José N. Iovino - 2014 - Annals of Pure and Applied Logic 165 (6):1169-1200.

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Citations of this work BETA

Fuzzy Logic.Petr Hajek - 2008 - Stanford Encyclopedia of Philosophy.

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