CONCEPTUAL FOUNDATIONS OF QUANTUM MECHANICS: THE ROLE OF EVIDENCE THEORY, QUANTUM SETS, AND MODAL LOGIC

Germano Resconi (), George J. Klir and Eliano Pessa ()
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Germano Resconi: Department of Mathematics and Physics, Catholic University, Via Trieste 17, Brescia, Italy
George J. Klir: Center for Intelligent Systems and Department of Systems Science & Industrial Engineering, Thomas J. Watson School of Engineering and Applied Science, Binghamton University-SUNY, New York 13902-6000, USA
Eliano Pessa: ECONA, Interuniversity Center for Research on Cognitive Processing in Natural and Artificial Systems and Department of Psychology, University of Rome "la Sapienza", Via dei Marsi 78, 00185 Rome, Italy

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 01, 29-62

Abstract: Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

Keywords: Quantum mechanics; Evidence theory; Quantum logic; Modal logic; Possible worlds; Quantum sets (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000048

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