Degree-preserving Gödel logics with an involution: intermediate logics and (ideal) paraconsistency
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...
| Autores: | , , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/225436 |
| Acceso en línea: | https://hdl.handle.net/2445/225436 https://doi.org/10.1007/978-3-030-71258-7_6 |
| Access Level: | acceso abierto |
| Palabra clave: | Lògica algebraica Lògica matemàtica Algebraic logic Mathematical logic |
| Sumario: | 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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