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On fuzzy hidden variables. (English) Zbl 1079.81008
Fuzzy system is a couple \((E,S)\) consisting of a \(\sigma\)-orthocomplete effect algebra \(E\) and an order determining set \(S\) of \(\sigma\)-additive states on \(E\). Hidden variables (quasi-hidden variables, respectively) are defined in terms of embedding the system into a fuzzy system based on a tribe of fuzzy sets (based on a \(\sigma\)-MV algebra, respectively). Characterization of fuzzy systems admitting hidden variables (quasi-hidden variables, respectively) by means of a generating family of \(\sigma\)-additive (finitely additive, respectively) prime states is given. Bell-type inequalities are defined and their relations to hidden variables are shown.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
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