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Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
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In this paper, we study intermediate logics between the logic $\mathrm{G}_{\sim}^{\leq}$, the degree-preserving companion of Gödel fuzzy logic with involution $\mathrm{G}_{\sim}$, and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts $\mathrm{G}_{n \sim}^{\leq}$. Although $\mathrm{G}_{\sim}^{\leq}$ and $\mathrm{G}_{n \sim}^{\leq}$are explosive w.r.t. Gödel negation $\neg$, they are paraconsistent w.r.t. the involutive negation $\sim$. 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 $\mathrm{G}_{n \sim}^{\leq}$and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued $\L$ukasiewicz logics.
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Coniglio, M.E., Esteva, F., Gispert, J., Godo, L. (2021). Degree-Preserving Gödel Logics with an Involution: Intermediate Logics and (Ideal) Paraconsistency. In: Arieli, O., Zamansky, A. (eds) Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Outstanding Contributions to Logic, vol 21. Springer, Cham. ISBN: 978-3-030-71258-7. https://doi.org/10.1007/978-3-030-71258-7_6
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CONIGLIO, Marcelo e., ESTEVA MASSAGUER, Francesc, GISPERT BRASÓ, Joan, GODO I LACASA, Lluís. Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency. _Capítol del llibre: Arieli_. O.. Vol. Zamansky, núm. (eds) Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. [consulta: 2 de febrer de 2026]. [Disponible a: https://hdl.handle.net/2445/225436]