The set of [alpha]-orientations of a plane graph has a natural
distributive lattice structure.
The basic concept behind this ordering is
distributive lattice with their relations.
If distributive laws hold in a lattice then it is called a
distributive lattice.
Wu: Fuzzy ideals on a
distributive lattice, Fuzzy Sets and Systems, 35(1990), 231-240.
J] is a
distributive lattice, then the length function l also serves as a rank function, so [W.
L always denotes a completely
distributive lattice and if the lattices L does not contain the zero element and unit element I
5] Every
distributive lattice is a modular lattice.
If we order P (seen as a set of sets of worlds) by [contains or equals to], we obtain a complete
distributive lattice (P, [contains or equals to]) with the sentence F at the top and the sentence T at the bottom.
The concept of modular lattice,
distributive lattice, super modular lattice and chain lattices can be had from [14].
Finally, in Section 5 we make some remarks about a new partial order on TSSCPPs obtained via boolean triangles, which reduces in the permutation case to the
distributive lattice which is the product of chains of lengths 2, 3, .
l) if and only if S is a subdirect product of
distributive lattice and a member in [?
Farley and Schmidt answer a similar question for
distributive lattices in [6].
