  The concept of operator left residuation has been introduced by the authors
in a previous paper. Modifications of so-called quantum structures, in
particular orthomodular posets, like pseudo-orthomodular, pseudo-Boolean and
Boolean posets are investigated here in order to show that they are operator
left residuated or even operator residuated. In fact they satisfy more general
sufficient conditions for operator residuation assumed for bounded posets
equipped with a unary operation. It is shown that these conditions may be also
necessary if a generalized version using subsets instead of single elements is
considered. The above listed posets can serve as an algebraic semantics for the
logic of quantum mechanics in a broad sense. Moreover, our approach shows
connections to substructural logics via the considered residuation.
