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Non-Kolmogorovian approach to the context-dependent systems breaking the classical probability law.
Tokyo University of Science.
Linnaeus University, Faculty of Technology, Department of Mathematics. (mathematics)
Linnaeus University, Faculty of Technology, Department of Mathematics. (mathematgics)ORCID iD: 0000-0002-9857-0938
Tokyo University of Science.
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2013 (English)In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 43, no 7, 895-911 p.Article in journal (Refereed) Published
Abstract [en]

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

Place, publisher, year, edition, pages
2013. Vol. 43, no 7, 895-911 p.
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-28191DOI: 10.1007/s10701-013-9725-5ISI: 000320822400006Scopus ID: 2-s2.0-84879298558OAI: oai:DiVA.org:lnu-28191DiVA: diva2:641102
Available from: 2013-08-15 Created: 2013-08-15 Last updated: 2017-12-06Bibliographically approved

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Basieva, IrinaKhrennikov, Andrei

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