Semi-DeMorgan algebras are a common generalization of DeMorgan algebras and pseudocomplemented distributive lattices. A duality for them is developed that builds on the Priestley duality for distributive lattices. This duality is then used in several applications. The subdirectly irreducible semi-DeMorgan algebras are characterized. A theory of partial diagrams is developed, where properties of algebras are tied to the omission of certain partial diagrams from their duals. This theory is then used to find and give axioms for the largest variety of (...) semi-DeMorgan algebras with the congruence extension property. (shrink)

Finite demi-p-lattices are described in terms of the poset of its join irreducible elements endowed with a suitable set of maps. Description of the free algebras of demi-p-lattices and almost-p-lattices with n free generators are given.