2021/06/18 by Henrique Antunes, Abílio Rodrigues, Antunes, H. +5
Computer Science · #03B53 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2106.09850
openalex publication_date 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces the logic QLETF, a quantified extension of the logic of evidence and truth LETF, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LETF 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 \bullet, dual to each other: while ∘ A entails that A behaves classically, \bullet A follows from A's violating some classically valid inferences. The semantics of QLETF 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.