Algebras and Semantics for Dual Negations

Dunn investigated algebras and semantics for negations in non-classical logics. This paper extends his investigation to dual negations, more exactly to duals to the negations in Dunn [3, 5]. I first survey and systematize the algebras of dual negations, i.e., (self-dual) subminimal negation, dual Galois negations, dual minimal negation, wB (or dual intuitionistic) negation, (self-dual) De Morgan negation, and (self-dual) ortho negation, based on partially ordered sets. I next provide dual-perp semantics for these (dual) negations. I finally give representations for them by using dual-perp semantics.