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Since circuits and processors are heavily influenced and designed based upon boolean logic, which is itself a subset of propositional logic, could there be different interpretations of hardware or software based on another logic, like linear temporal logic or a description logic?

I mean, for example, could it be possible to apply the concepts of a different logic to come up with a new kind of compiler or digital circuits or even a new processor architecture based on a non-classical logic?

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Computers make heavy use of sequential logic (as opposed to combinatorial). Isn't this an instance of temporal logic ?

One might think of implementing fuzzy logic in hardware, which would be reminiscent of analog computers. But I can't see the benefit.

Tri-state logic computers have been tried. And abandoned due to the excessive complexity.

Nothing beats good old zeroes and ones. I did not notice that any non-classical logic became pervasive in any domain.

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