??so what about "b-valued existence and equality predicates ..." (and so forth ...) and .... :

1 ??something about "kripke model" or something....

2 ??something about propositional theory ...

3 ??something about interpretation of quantifier ...

4 ??something about ... ??well, maybe nice simple example of #3, or something.... ??theory of "for all x there exists y st r(x,y)" ... or something ...

?? and so forth .... ???...

???something about ... ??"orthogonal partitions" and malcheff variety or something, and so forth .... ????...

something about mere oder up / downset , vs ... ??more ... ???...

and so forth ... ???....