Many-Valued Points And Equality

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper we present some conservative translations involving classical logic, Lukasiewicz three-valued system L₃, the intuitionistic system I¹ and several paraconsistent logics, as for instance Sette's system P¹, the D'Ottaviano and da Costa system J₃ and da Costa's systems C_n, 1 n.