Quasi-orthomodular Posets and Weak BCK-algebras

A quasi-orthomodular poset is defined to be a poset with 0 equipped with an orthogonality relation satisfying certain axioms. The goal of the paper is to compare such posets (also semilattices, nearlattices and lattices) with several other kinds of posets having an appropriate structure and already known in the literature: generalized orthomodular posets and lattices, generalized orthoalgebras, sectionally orthocomplemented, sectionally orthomodular and relatively orthocomplemented posets and meet semilattices, semi-orthomodular lattices, weak BCK-algebras.