  Since orthomodular posets serve as an algebraic axiomatization of the logic
of quantum mechanics, it is a natural question how the connective of
implication can be defined in this logic. It should be introduced in such a way
that it is related with conjunction, i.e. with the partial operation meet, by
means of some kind of adjointness. We present here such an implication for
which a so-called unsharp residuated poset can be constructed. Then this
implication is connected with the operation meet by the so-called unsharp
adjointness. We prove that also conversely, under some additional assumptions,
such an unsharp residuated poset can be converted into an orthomodular poset
and that this assignment is nearly one-to-one.
