Problem of Existence of Joint Distribution on Quantum Logic

This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, which is a mathematical tool suitab...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2024-12, Vol.26 (12), p.1121
Main Authors: Nánásiová, Oľga, Čipková, Karla, Zákopčan, Michal
Format: Article
Language:English
Subjects:
Algebra
Analysis
Boolean
Boolean algebra
Functions (mathematics)
generalized probability
joint distribution
Logic
marginal distribution
non-compatibility
Probability
probability space
quantum logic
Random variables
Citations: Items that this one cites
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Summary:This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, which is a mathematical tool suitable for constructing virtual joint probabilities of even non-compatible propositions. The paper completes conclusions published in 2020 and extends the results for three or more random variables if the marginal distributions are known. The existence of a (n+1)-variate joint distribution is shown in special cases when the quantum logic consists of at most n blocks of Boolean algebras.
ISSN:1099-4300
1099-4300
DOI:10.3390/e26121121