Modality and Contextuality in Topos Quantum Theory

Studia Logica 104 (6):1099-1118 (2016)
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Topos quantum theory represents a whole new approach to the formalization of non-relativistic quantum theory. It is well known that TQT replaces the orthomodular quantum logic of the traditional Hilbert space formalism with a new intuitionistic logic that arises naturally from the topos theoretic structure of the theory. However, it is less well known that TQT also has a dual logical structure that is paraconsistent. In this paper, we investigate the relationship between these two logical structures and study the implications of this relationship for the definition of modal operators in TQT.



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Benjamin Eva
Duke University

References found in this work

Interpreting the Modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics.Christian de Ronde, Hector Freytes & Graciela Domenech - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 45:11-18.
Bi-Heyting algebras, toposes and modalities.Gonzalo E. Reyes & Houman Zolfaghari - 1996 - Journal of Philosophical Logic 25 (1):25 - 43.
Modal propositional logic on an orthomodular basis. I.L. Herman & R. Piziak - 1974 - Journal of Symbolic Logic 39 (3):478-488.

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