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Fuzzy quantum spaces and compatibility. (English) Zbl 0657.60004
Using ideas from mathematics for fuzzy systems, the authors generalize the notion of probability quantum space introduced by P. Suppes [see Philos. Sci. 33, 14-21 (1966)] to so-called fuzzy quantum spaces. The main goal of their paper is to present conditions for the ranges of observables in a fuzzy quantum space to have classical character, i.e. to be embeddable into some Boolean \(\sigma\)-algebra.
This question is known as the compatibility problem and it has been solved for different classes of quantum logics using different notions of compatibility. Here it is shown that for finite compatible observables in any fuzzy quantum space joint-observables always exist.
Reviewer: K.Piasecki

MSC:
60A99 Foundations of probability theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
03E72 Theory of fuzzy sets, etc.
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