Quantum Mechanics rather famously has problems in interpretation - straightforward realism doesn't appear to work. Is there any work with modal logic that throws light on this question?

The SEP has an entry on modal interpretations of QM. But a quick scan through doesn't show any immediate work with modal logic.

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    You might be interested in quantum logic if you aren't already familiar with it. – Dennis Mar 13 '13 at 21:31
  • @Dennis: I'm vaguely familiar from my studies of QM (quite some time ago); my impression was that von Neumann had spotted formal similarities & dis-similarities between QM (its space of projection operators) & Logic which to my mind didn't add up to a logic as there is no interpretation - that of course doesn't mean that it isn't an interesting bridge and core (its dynamical and statistical properties are fixed). The SEP says that its a non-classical probability calculus on top of a non-classical propositional logic (which is an orthocomplemented lattice – Mozibur Ullah Mar 14 '13 at 0:39
  • @Dennis: I can see what this means in Hilbert Space but what does it mean as a propositional logic? Do you know if there is a formal named non-classical logic that is identified with this? Projections that commute appear to generate a classical logic. – Mozibur Ullah Mar 14 '13 at 0:51
  • @Dennis: Scotch that question. It's its similarity to a boolean lattice which must have got von Neumann thinking and those lattices are equivalent to propositional logics. – Mozibur Ullah Mar 14 '13 at 5:12

There certainly has been a large amount of development of modal logic interpretations of Quantum Mechanics. Once you have a Kripkean accessibility relationship (induced from nonorthogonality), the development is simple. Early work here is Goldblatt - "Semantic analysis of orthologic" Journal of Philosophical Logic (1974) and "The Stone space of an ortholattice" Bulletin of the London Mathematical Society (1975), and Dalla Chiara - "Quantum logic and physical modalities" Journal of Philosophical Logic (1977) and "Physical implications in a Kripkean semantical approach to physical theories" Logic in the 20th Century (1983). The basic idea to obtain the accessibility relations uses work from Foulis and Randall on lexicographic orthogonality, as it's not so simple to avoid what would become "extended probabilities" in a counterfactual view of separated events to build the modal relationship.

It is important to make some distinctions with the work described on the page you linked. That research programme is linked with modality in the view of possibilities as a means of regaining realist foundations. That's an involved program that delves into operationalist interpretations and can indeed be used to build modal operators as one is familiar with in modal logic. In fact, there are S4 interpretations on the surface of most operationalist approaches. However, that is not quite the same things as the modal operators of the quantum events themselves, based on the standard orthomodular logical foundation. My first paragraph deals with the latter program.

  • I was expecting 'consistent histories' to appear here, but I see that you've tied that up with sheafs! I realised that there was some kind of distinction - but hadn't pinned it down. – Mozibur Ullah Mar 14 '13 at 0:55

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