Truth Values of Quantum Phenomena

In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic must be decided: the problem of choosing a proper system of many-valued logic and the problem of the emergence of bivalence from logical many-valuedness. Difficulties accompanying solutions of these problems are discussed.

[1]  S. Gottwald.  A Treatise on Many-Valued Logics , 2001 .

[2]  Abubakr Gafar Abdalla,et al.  Probability Theory , 2017, Encyclopedia of GIS.

[3]  K. Jung.  Is the de Broglie-Bohm interpretation of quantum mechanics really plausible? , 2013 .

[4]  F. Holik,et al.  Classical Limit and Quantum Logic , 2018 .

[5]  D. Bohm.  A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

[6]  E. Beltrametti,et al.  Bericht: On the Logic of Quantum Mechanics , 1973 .

[7]  S. Kochen.  A Reconstruction of Quantum Mechanics , 2013, Synthese Library.

[8]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[9]  Rafael D. Sorkin.  An exercise in "anhomomorphic logic" , 2007 .

[10]  B. M. Hill,et al.  Theory of Probability , 1990 .

[11]  I. Pitowsky.  Quantum Probability ― Quantum Logic , 1989 .

[12]  Jarosław Pykacz,et al.  Fuzzy quantum logics and infinite-valued Łukasiewicz logic , 1994 .

[13]  N. P. Landsman.  Between classical and quantum , 2005 .

[14]  Jaroslaw Pykacz,et al.  Łukasiewicz Operations in Fuzzy Set and Many-Valued Representations of Quantum Logics , 2000 .

[15]  Jaroslaw Pykacz,et al.  Towards many-valued/fuzzy interpretation of quantum mechanics , 2011, Int. J. Gen. Syst..

[16]  Jeffrey Bub,et al.  A Proposed Solution of the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory , 1966 .

[17]  Charles G. Morgan,et al.  Probability theory, intuitionism, semantics, and the Dutch book argument , 1983, Notre Dame J. Formal Log..

[18]  Jaroslaw Pykacz,et al.  Can Many-Valued Logic Help to Comprehend Quantum Phenomena? , 2014, 1408.2697.

[19]  The Problem of Conjunction and Disjunction in Quantum Logics , 2017 .

[20]  Jaroslaw Pykacz,et al.  Unification of Two Approaches to Quantum Logic: Every Birkhoff – von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic , 2010, Stud Logica.

[21]  Lukasiewicz Logic.  Quantum Logic as Partial Infinite-Valued , 1995 .

[22]  G. Francis.  Foundations of Statistics Week 10: Regression , 2012 .

[23]  D. Michael Miller,et al.  Multiple Valued Logic: Concepts and Representations , 2008, Multiple Valued Logic.

[24]  H. Jeffreys,et al.  Theory of probability , 1896 .

[25]  D. G. Rees,et al.  Foundations of Statistics , 1989 .

[26]  Carlton M. Caves,et al.  Subjective probability and quantum certainty , 2006 .