A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3$$_{\text {DH}}$$

Abstract

The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic B $$_{\text {M}}$$ with a dual intuitionistic negation of the type Sylvan defined for the extension CC $$\omega $$ of da Costa’s paraconsistent logic C $$\omega $$ . We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3 $$_{\text {DH}}$$ , the expansion of G3 $$_{+}$$ with a dual intuitionistic negation of the kind considered by Sylvan (G3 $$_{+}$$ is the positive fragment of Godelian 3-valued logic G3). All logics in the paper are paraconsistent.