M. E. Coniglio | Searcharxiv

arXiv2026

Degree-preserving Godel logics with an involution: intermediate logics and (ideal) paraconsistency

In this paper we study intermediate logics between the degree preserving companion of Godel fuzzy logic with an involution and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts. Although these degree-preserving Godel logics are explosive with respect to Godel negation, they are paraconsistent with respect to the involutive negation. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between the degree-preserving n-valued Godel fuzzy logic with an involution and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued Lukasiewicz logics.

cs.LO↗

arXiv2021

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

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.

math.LO↗