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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.

MSC:
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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