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.

从彼得·哈耶克（PetrHájek）关于数学模糊逻辑的著作出发，过去二十年来，几位作者已经开发了分级模型理论，作为对研究多值谓词逻辑语义的经典模型理论的扩展。在本文中，我们朝着对该模型理论的抽象表述迈出了第一步。我们给出了基于多值模型的抽象逻辑的一般概念，并证明了从逻辑特性（如紧凑性，抽象完整性，Löwenheim-Skolem特性，Tarski联合特性）方面对一阶逻辑的最大值的六个Lindström风格表征。 ，以及Robinson财产等。作为必要的技术限制，我们假设模型是在有限的MTL链上赋值的，并且语言的每个真值均具有常数。