Some results on BZ structures from Hilbertian unsharp quantum physics

Foundations of Physics 25 (8):1147-1183 (1995)
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Abstract

Some algebraic structures determined by the class σ(þ) of all effects of a Hilbert space þ and by some subclasses of σ(þ) are investigated, in particular de Morgan-Brouwer-Zadeh posets [it is proved that σ(þ n )(n<∞) has such a structure], Brouwer-Zadeh * posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh 3 posets which are both de Morgan and *.It is shown that a nontrivial class of effects of a Hilbert space exists which is a BZ 3 poset. An ɛ-preclusivity relation on the set of all vectors of þ is introduced, and it is shown that it satisfies the regularity condition also for ε∃ [1/2, 1]

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References found in this work

Semantic analysis of orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
The Interpretation of Quantum Mechanics.E. Levy - 1976 - Canadian Journal of Philosophy 6 (1):161-175.
Paraconsistent quantum logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1989 - Foundations of Physics 19 (7):891-904.
The Interpretation of Quantum Mechanics.Jeffrey Bub - 1978 - Erkenntnis 12 (3):399-402.

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