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Is quantum logic producing interesting/different mathematics?

Is it different from the intuitionist approach to mathematics? How?

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    I don't think people use quantum logic that way, but I could be wrong.2011-02-27

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There is an approach to quantum logic where you get topoi with quantum logic. An elementary topos is sometimes regarded as a "place" where you can do mathematics, but where classical logic doesn't necessarily apply. Thus you get a different sort of mathematics.

I know very little about these quantum topoi, so I cannot detail in what way their mathematics differ from the classical one. But I think the two articles referenced in the below PlanetMath articles may (or may not - I haven't read them) answer your question.

http://planetmath.org/encyclopedia/QuantumLogicsTopoi2.html

http://planetmath.org/encyclopedia/QuantumStateSpace.html