A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3 DH

The logic DHb is the result of extending Sylvan and Plumwood's minimal De Morgan logic BM with a dual intuitionistic negation of the type Sylvan defined for the extension CCω of da Costa's paraconsistent logic Cω. We provide Routley-Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3DH the expansion of G3₊ with a dual intuitionistic negation of the kind considered by Sylvan (G3₊ is the positive fragment of Gödelian 3-valued logic G3). All logics in the paper are paraconsistent.