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On a characterization of probability measures on Boolean algebras and some orthomodular lattices. (English) Zbl 0848.03034
Bell-type inequalities in Boolean algebras and in horizontal sums of Boolean algebras are studied. In particular, the authors present the number of Bell-type inequalities with integer-valued coefficients holding in all finite Boolean algebras. Finally, the possibility of extension of positive-valued mappings defined on generators of finite Boolean algebras is studied.

03G12 Quantum logic
03G05 Logical aspects of Boolean algebras
06C15 Complemented lattices, orthocomplemented lattices and posets
81P15 Quantum measurement theory, state operations, state preparations
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