We study Bell-type inequalities of order n with emphasis on the case n = 2 in the framework of the structure of an orthomodular lattice, which is a logicoalgebraic model of quantum mechanics. We give necessary and sufficient conditions for the validity of Bell-type inequalities of order 2. In particular, we study Bell-type inequalities in various structures connected with a Hilbert space, and we give a characterization of Boolean algebras via the validity of certain Bell-type inequalities. [References: 39]
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