Priestley duality for some algebras with a negation operator

Abstract

In [1], the variety of ¬-lattices was introduced as a bounded distributive lattices, A, endowed with a unary operation ¬, satisfying the axioms ¬0 ≈ 1 and ¬ (a ∨ b) ≈ ¬a ∧ ¬b. In this paper, we apply the representation and the duality developed in [1] to give short representations for semi-De Morgan algebras, demi-p-lattices, almost p-lattices, and weak Stone algebras.