It's probably nothing, but one of the pivotal lemmas is (a|(a|(a|b))) = (a|b). Imagine replacing (a|b) with x to get (a|(a|x)) = x; then this identity can be re

It's probably nothing, but one of the pivotal lemmas is (a|(a|(a|b))) = (a|b). Imagine replacing (a|b) with x to get (a|(a|x)) = x; then this identity can be read as "x reflected through 'a' twice gives x". It reminds me of O Loos's axiomatic approach to Symmetric Spaces where the operation | means reflect. It axioms are (x|x) = x; (x|(x|y)) = y; (x|(y|z)) = ((x|y)|(x|z)); and finally that "|" should be a smooth function over some manifold. But then again, when "|" is NAND, it follows that (a|b)|(a|b) means NOT (a|b), which breaks the apparent link to symmetric spaces, because x reflected through itself should give back x.