Degree-Preserving Gödel Logics with an Involution: Intermediate Logics and (Ideal) Paraconsistency
This study investigates intermediate logics situated between degree-preserving Gödel fuzzy logic with involution and classical propositional logic, focusing on their paraconsistent behavior relative to involutive negation in the finite-valued setting. By introducing “saturated paraconsistency”—a notion strictly weaker than ideal paraconsistency—and combining tools from algebraic logic, the classification of intermediate logics, and finite-valued fuzzy logic, the work fully characterizes the boundaries of all ideal and saturated paraconsistent logics lying between the n-valued Gödel involutive logic and classical logic. Furthermore, it identifies a broad class of saturated paraconsistent logics within intermediate systems of finite-valued Łukasiewicz logic.