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arXiv · 2106.09850

Valuation semantics for first-order logics of evidence and truth (and some related logics)

H. Antunes·A. Rodrigues·W. Carnielli·M. E. Coniglio
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Abstract

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 ${\circ}$ and a non-classicality operator $\bullet$, dual to each other: while ${\circ} A$ entails that $A$ behaves classically, ${\bullet} A$ 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.

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H. Antunes, A. Rodrigues, W. Carnielli, M. E. Coniglio. 2021-06-18. Valuation semantics for first-order logics of evidence and truth (and some related logics). https://arxiv.org/abs/2106.09850

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