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  1. Bell-Type Inequalities for Bivariate Maps on Orthomodular Lattices.Jarosław Pykacz, L’Ubica Valášková & Ol’ga Nánásiová - 2015 - Foundations of Physics 45 (8):900-913.
    Bell-type inequalities on orthomodular lattices, in which conjunctions of propositions are not modeled by meets but by maps for simultaneous measurements -maps), are studied. It is shown, that the most simple of these inequalities, that involves only two propositions, is always satisfied, contrary to what happens in the case of traditional version of this inequality in which conjunctions of propositions are modeled by meets. Equivalence of various Bell-type inequalities formulated with the aid of bivariate maps on orthomodular lattices is studied. (...)
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  • Can many-valued logic help to comprehend quantum phenomena?Jarosław Pykacz - unknown
    Following Lukasiewicz, we argue that future non-certain events should be described with the use of many-valued, not 2-valued logic. The Greenberger - Horne - Zeilinger 'paradox' is shown to be an artifact caused by unjustified use of 2-valued logic while considering results of future non-certain events. Description of properties of quantum objects before they are measured should be performed with the use of propositional functions that form a particular model of infinitely-valued Lukasiewicz logic. This model is distinguished by specific operations (...)
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