An Algebraic Approach to Non-classical Logics

Preliminary set-theoretical, topological and algebraic notions. Topological spaces. Ordered sets and quasi-ordered sets. Implicative algebras. definition and elementary properties. Positive implication algebras. Implicative filters in positive implication algebras. Distributive lattices and quasi-boolean algebras. Distributive lattices. Quasi-boolean algebras. Relatively pseudo-complemented lattices, contrapositionally complemented lattices, semi-complemented laticies and pseudo-boolean algebras. Quasi-pseudo-boolean algebras. Boolean algebras and topological boolean algebras. Post algebras. Implicative extensional propositional calculi. Positive implicative logic and classical implicative logic.