Has there been any research done along these lines? A (the?) name that pops up repeatedly in paraconsistency and physics is that of Newton da Costa (with collaborators). Here are some references to his and others' work. Remarks on the applications of paraconsistent logic to ph...
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In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\ -D.\ F\'evrier's 'logic of complementarity' as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed 'paraclassical logic'.