On superintuitionistic propositional logics connected with partially ordered sets

This paper introduces a new method of representing pseudo-Boolean algebras by implication structures of a special type or by partially ordered sets. This is used to construct four sequences of pseudo-Boolean algebras. Their properties and the properties of the logics prescribed by the sequences are studied. The connection between these logics and the logic consisting of the realizable propositional formulas is established, and a problem posed by Hosoi and Ono is solved.