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Minimal and maximal sets of Bell-type inequalities holding in a logic. (English) Zbl 0862.03040
Let $$p$$ be a state on a quantum logic $$L$$ (= orthomodular lattice). Let $$n$$ be an integer, $$N=\{1,\dots,n\}$$ and $$f:2^N\to Z$$. A Bell-type inequality is an inequality $\sum_{I\subseteq N}f(I) p(\bigwedge_{i\in I}a_i)\in [0,1],$ $$a_1,\dots, a_n\in L$$. The authors show that the class of all functions $$f:2^N\to Z$$ which give a Bell-type inequality, has a smallest and a greatest element.
##### MSC:
 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 06C15 Complemented lattices, orthocomplemented lattices and posets
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