 structure of lattices?  Or, do your &quot;languages&quot;
    exclude cyclic relationships?

Not sure what you are after here.

For future reference:

| Lattice.
|
| When x and y are elements of an ordered set L,
| the supremum and infimum of {x, y}, whenever
| they exist, are called the &quot;join&quot; and &quot;meet&quot;
| of x, y and denoted by x |_| y and x |^| y,
| respectively.  L is called a &quot;lattice&quot; (or
| &quot;lattice-ordered set&quot;) when every pair of
| its elements has a join and