This paper introduces the logic QLET_F, a quantified extension of the logic of evidence and truth LET_F, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LET_F is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘A entails that A behaves classically, ∙A follows from A’s violating some classically valid inferences. The semantics of QLET_F combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of FDE, K3, and LP, we show how these tools, which we call here the method of anti-extensions + valuations, can be naturally applied to a number of non-classical logics.

本文介绍了逻辑Q L E T _F ，它是证据和真相逻辑L E T _F的量化扩展，以及相应的健全和完整的一阶非确定性估值语义。L E T _F是一种准一致且准完备的句子逻辑，它扩展了一级蕴涵 ( FDE ) 的逻辑，其中经典算子 ∘ 和非经典算子 ∙ 彼此对偶：而 ∘ A蕴涵A表现经典， ∙ A源自A违反了一些经典有效的推论。Q L E T _F的语义结合了根据反扩展解释否定谓词的结构与一阶非确定性估值，并且通过 Henkin 方法的推广获得完整性。通过为FDE、K3和LP的一阶扩展提供健全和完整的语义，我们展示了这些工具，我们在这里称之为反扩展+估值方法，可以自然地应用于许多非经典逻辑.