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.

翻译：本文研究了具有对合的哥德尔模糊逻辑的度保持伴随逻辑与经典命题逻辑CPL之间的中间逻辑，以及它们的有限值对应逻辑的中间逻辑。尽管这些度保持哥德尔逻辑相对于哥德尔否定是爆炸性的，但相对于对合否定它们是次协调的。我们引入了饱和次协调性的概念，这是一个比理想次协调性更弱的概念，并完整刻画了具有对合的n值哥德尔模糊逻辑的度保持逻辑与CPL之间的理想次协调逻辑和饱和次协调逻辑。我们还识别了在度保持有限值Łukasiewicz逻辑的中间逻辑族中一个庞大的饱和次协调逻辑家族。