Quantum logic and probability theory

Abstract

The paper provides the review of the texts on quantum logic, the texts which are directly connected with the mathematical foundations of quantum mechanics. These are texts which discuss the theory of quantum probability. The development of the mathematical scheme of quantum mechanics is discussed along the following line: P.A.M. Dirack’s 1927 “The Principles of Quantum Mechanics”, J. von Neumann’s 1932 “Mathematische Grundlagen der Quantenmechanik”, G.Birkgoff-I.von Neumann’s 1936 “The logic of quantum mechanics”. It is shown that the further development of the mathematical foundations of quantum mechanics resulted in the construction of quantum theory of probability, the theory generalizing A.N.Kolmogorov’s classical probability and critically improving von Neumann’s 1932 mathematical scheme.