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Kripke semantics interpret intuitionistic logic by a partially ordered set of worlds/situations. Consistent histories interpretation of QM elaborates the copenhagen interpretation where a consistent set of histories can be assigned probabilities.

I don't really understand either of these formalisms, but it does appear on the face of it that the formalisms should have something in common, do they?

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    $\begingroup$ Check out the topos approaches to quantum mechanics, as initiated by Isham/Butterfield and Döring/Isham (the contravariant approach, see review by Flori: arxiv.org/abs/1106.5660). There's also a covariant approach, developed by Heunen, Landsman and Spitters (see Wolters' comparison of the approaches: arxiv.org/abs/1010.2031). That should get you started. $\endgroup$
    – Ulrik Buchholtz
    Commented Sep 22, 2012 at 16:52
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    $\begingroup$ Isham addresses the topic specifically in 'Topos Theory and Consistent Histories' arxiv.org/abs/gr-qc/9607069. $\endgroup$
    – David Corfield
    Commented Sep 23, 2012 at 14:34
  • $\begingroup$ great, thanks for both these references. $\endgroup$
    – Mozibur Ullah
    Commented Sep 23, 2012 at 17:11

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