Logical and algebraic properties of generalized orthomodular posets

Abstract Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of present paper in order to establish a useful tool for studying logic quantum mechanics. They investigated structural properties these posets. In paper, we study logical algebraic particular, investigate conditions under which they can be converted into operator residuated structures. Further, their representation means algebras (directoids) with everywhere defined operations. We prove congruence class assigned generalized and, subvariety this determined simple identity. Finally, contrast fact that Dedekind-MacNeille completion an poset need not lattice, show stronger version is nearly lattice.