The story is that in a lattice, there are some elements incomparable, and there exits some elements have overlapping elements. for example, suppose the partial order is defined on inclusion, then e1= {a,b} and e2 = {b,c}, they are incomparable, but they have common element b.
Thus, for this kind of lattice elements, I want to be able to compute the difference between A and B say A - B.. What I can do is that I can define the complementation of the element in the lattice which A - B = A meet complementation of B.
Therefore, my question is that, how to define the subtraction operation in lattice? If I define the subtract with respect of complementation, then how can I actually compute it? I mean I can define the complementation of A is A', where A join A' = top and A meet A' = bot. But this does not give me much information how to actually compute the complementation!