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Łukasiewicz Operations in Fuzzy Set and Many-Valued Representations of Quantum Logics

Jarosław Pykacz

Foundations of Physics 30 (9):1503-1524 (2000)

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Can many-valued logic help to comprehend quantum phenomena?Jarosław Pykacz - unknowndetails 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 (...) Download Export citation Bookmark 4 citations
Emergent quantum indeterminacy.Cristian Mariani - 2021 - Ratio 34 (3):183-192.details Many features of quantum mechanics (QM) suggest that, at the microscopic level, objects sometimes fail to determinately instantiate their properties. In recent years, many have argued that this phenomenon indicates the existence of an ontological kind of indeterminacy, often called metaphysical indeterminacy, which is supposed to affect the ontology of QM. As insisted by Glick ('Against Quantum Indeterminacy), however, once we look at the major realist approaches to QM we learn that the indeterminacy disappears from the description of the world (...) Download Export citation Bookmark 5 citations
(1 other version)Unification of Two Approaches to Quantum Logic: Every Birkhoff -von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic.Jarosław Pykacz - 2010 - Studia Logica 95 (1-2):5 - 20.details In the paper it is shown that every physically sound Birkhoff - von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infini te-valued Lukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning. Download Export citation Bookmark 2 citations
(1 other version)Unification of Two Approaches to Quantum Logic: Every Birkhoff – von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic.Jarosław Pykacz - 2010 - Studia Logica 95 (1-2):5-20.details In the paper it is shown that every physically sound Birkhoff – von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infinite-valued Łukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning. Download Export citation Bookmark 2 citations
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.details 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. (...) Download Export citation Bookmark

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