  When an algebraic logic based on a poset instead of a lattice is investigated
then there is a natural problem how to introduce the connective implication to
be everywhere defined and satisfying (left) adjointness with the connective
conjunction. We have already studied this problem for the logic of quantum
mechanics which is based on an orthomodular poset or the logic of quantum
effects based on a so-called effect algebra which is only partial and need not
be lattice-ordered. For this, we introduced the so-called operator residuation
where the values of implication and conjunction need not be elements of the
underlying poset, but only certain subsets of it. However, this approach can be
generalized for posets satisfying more general conditions. If these posets are
even finite, we can focus on maximal or minimal elements of the corresponding
subsets and the formulas for the mentioned operators can be essentially
simplified. This is shown in the present paper where all theorems are explained
by corresponding examples.
