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Foundations of non-commutative probability theory [PDF]

Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge, 2009
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way.
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Foundations of a quantum probability theory

Journal of Mathematical Physics, 1975
Statistical physical theories are frequently formulated in terms of probabilistic structures founded on a ’’logic of experimentally verifiable propositions.’’ It is argued that to each experimentally verifiable proposition there corresponds an experimental procedure which, in general, alters the state of the system, and is completely characterized by a
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Foundations of Probability Theory

2009
This chapter contains sections titled: Historical Background Approaches to the Definition of Probability The Concept of Probability The Field of Events Classical Definition of Probability Random Variables Numerical Characteristics of Random Variables Basic Rules of Operation Computing Conditional ...
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Modal foundations of probability theory

Erkenntnis, 1981
In this paper I want to outline how the sequential logic introduced in [12] can serve as a syntactical basis for a non-classical modal logic. In a second step I shall found a probability theory on this modal logic in such a way that probabilities represent degrees of possibility. The three levels: sequen?
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Identical foundation of probability theory and fuzzy set theory

Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997), 2003
Information fusion introduces special operators o in probability theory and fuzzy theory. Some serious data certify in each case these two quite distinct techniques. The article shows that four postulates are the unique aim of these two theories. Evidence theory and fuzzy set theory often replace probabilities in medicine, economy and control.
D. de Brucq, O. Colot, A. Sombo
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Mathematical Foundations of Probability Theory

1984
The theory of probability, as a mathematical discipline, can and should be developed from axioms in exactly the same way as Geometry and Algebra. This means that after we have defined the elements to be studied and their basic relations, and have stated the axioms by which these relations are to be governed, all further exposition must be based ...
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Carnap's foundation of probability theory

Synthese, 1949
In 1945, in a paper in "Philosophy and Phenomenological Research", Rudolf Carnap made a distinction between two concepts of probability. One of these, called by him "probability2", is based in one form or another on frequency quotients of observed phenomena, whereas the other one, called "probabilityi", deals with a concept like "rational degree of ...
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The Empirical Foundations of Probability Theory

The Mathematics Teacher, 1973
It is desirable that scientifically oriented secondary and college students be exposed to the role played by mathematics in modeling physical theory and experiment. The nature of the probability model and the empirical evidence offered to support its applications can furnish a very effective counterpoint to the standard examples of the empirical ...
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Foundations of Probability Theory

2022
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Foundations of a new system of probability theory

Topoi, 1986
The aim of my book is to explain the content of the different notions of probability. Based on a concept of logical probability, which is modified as compared with Carnap, we succeed by means of the mathematical results of de Finetti in defining the concept of statistical probability. The starting point is the fundamental concept that certain phenomena
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