  As algebraic semantics of the logic of quantum mechanics there are usually
used orthomodular posets, i.e. bounded posets with a complementation which is
an antitone involution and where the join of orthogonal elements exists and the
orthomodular law is satisfied. When we omit the condition that the
complementation is an antitone involution, then we obtain skew-orthomodular
posets. To each such poset we can assign a bounded lambda-lattice in a
non-unique way. Bounded lambda-lattices are lattice-like algebras whose
operations are not necessarily associative. We prove that any of the following
properties for bounded posets with a unary operation can be characterized by
certain identities of an arbitrary assigned lambda-lattice: complementarity,
orthogonality, almost skew-orthomodularity and skew-orthomodularity. It is
shown that these identities are independent. Finally, we show that the variety
of skew-orthomodular lambda-lattices is congruence permutable as well as
congruence regular.
