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I'm learning digital engineering and I'm also a fan of theoretical and abstract physics and mathematics. I find it amazing that you have an algebra that directly corresponds to logic circuits and if you do manipulations on paper you can see the direct result on the circuits. So I wondered if there is a generalisation of all of this, or even a kind of higher dimensional digital electronics or something like that. My guess is that it must be some kind of generalised boolean algebra, but not sure. Any suggestions? I already asked this in electrical engineering stack exchange, but I think this question may a be over the heads of the engineers there.

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    $\begingroup$ So how is this related to physics? $\endgroup$ – Emilio Pisanty Oct 16 '15 at 21:32
  • $\begingroup$ Removing the requirement of existence of a unit from the axioms of Boolean algebra yields "generalized Boolean algebras" $\endgroup$ – user83548 Oct 16 '15 at 21:32
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    $\begingroup$ A structure that satisfies all axioms for Boolean algebras except the two distributivity axioms is called an orthocomplemented lattice. Orthocomplemented lattices arise naturally in quantum logic as lattices of closed subspaces for separable Hilbert spaces. $\endgroup$ – user83548 Oct 16 '15 at 21:33
  • $\begingroup$ Crossposted from electronics.stackexchange.com/q/195706/52589 $\endgroup$ – Qmechanic Oct 16 '15 at 22:04
  • $\begingroup$ Echoing bruce smitherson's above comment, Quantum/fuzzy logic generalizes classical Boolean logic. $\endgroup$ – Qmechanic Nov 11 '15 at 20:19

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