[jonsen]

And so does

  MAX(a,MIN(b,c)) = MIN(MAX(a,b),MAX(a,c))

so it is even more useful than normal algebra :p

[homegarlic]

Fuzzy logic has insane amounts of similar ORs and ANDs that also have to conform some simple laws.

Generalization of ANDs and ORs is called t-norms and t-conorms (s-norms). They have to satisfy laws of monotonicity, commutativity and associativity.

So all kinds of magical ANDs and ORs spawn to meet the requirements.

I'm not really a fan of fuzzy logic but it really is a nice exercise in mathematics.