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Paraconsistent ideas in quantum logic. (English) Zbl 0969.03070

Birkhoff and von Neumann’s quantum logic is sharp in the sense that propositions correspond to exact possible properties of the physical system under investigation. Unsharp approaches to quantum theory were proposed by G. Ludwig [Foundations of quantum mechanics, Vol. 1, Springer, Berlin (1983; Zbl 0509.46057)] and developed by Kraus, Davies, Mittelstaedt, Busch, Lahti, Bugajski, Beltrametti, Cattaneo and many others. This paper surveys effect structures and unsharp quantum logics, to which the authors themselves have contributed much.

MSC:

03G12 Quantum logic
03B53 Paraconsistent logics
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)

Citations:

Zbl 0509.46057
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