*
|MAX (P=1)
|
|
max* 12 (P=7/8 =1/2+3/4-1/2*3/4) (complemented)
/ \ (join reducible to 4-node & 6-node)
/ \
(parordering)-> / \
/ \<--(parordering)
/ \
/ \
(complemented) (P=1/2) 4 * * 6 (P=3/4=1/4+1/2-1/4*1/2 by INCLUSION-EXCLUSION Principle.)
(proper join irreducible) | /| (comoplemented, join reducible to 2-node & 3-node)
(improper atom) | / |
| / |
| / |
(not parordering but simple)->| / |
| / |
| / | <-- (parordering)
| / |
| / |
| / |
| / |
| /<-(parord.)|
|/ |
(noncomplemented) (P=1/4) 2 * * 3 (P=1/2) (complemented)
(improper join irreducible, \ | (improper join irreducible,
proper atom) \ / proper atom)
(meet of 4-node & 6-node) \ /
\ /
\ /
\ /
\ /
\/
min* 1 (P=1/8=1/4*1/2) (complemented)
| (meet of 2-node & 3-node)
|
|
*MIN (P=0)
(Note: Complemented atoms are assigned equiprobabilites = equifractions of 1. Noncomplemented atoms in a LINE successively HALVE the value assigned to their Complemented atom. The MAX and min of a lattice are ideal or limit points never attained by join or meet operations. Hence, the 0, 1 probabilities are ideal or limit values, never attained by THE INCLUSION-EXCLUSION PRINCIPLE.)