A paraconsistent 3-valued logic related to Godel logic G3
Gemma Robles, José M. Méndez · Logic Journal of IGPL · 2013
The aim of the article is to introduce a paraconsistent logic, G3<Ł, related to Gödel 3-valued logic G3. In order to adequately explain G3<Ł, the akin logics G3Ł(FD) and G31Ł are also investigated. A Henkin-style completeness proof is provided for each one of these logics by endowing them with dually equivalent under-determined and over-determined bivalent semantics of the type defined by Dunn. G3Ł(FD), G31Ł and G3<Ł are related to ‘quasi relevant’ logics such as R-Mingle or RM3, as well as to non-relevant logics such as Łukasiewicz Ł3 or some logics in the vicinity of intuitionistic logic. The logic G3<Ł belongs to the class of paraconsistent logics extending positive intuitionistic logic rather than positive classical logic.