Title: Logical probabilistic analysis and its history

Authors: Igor A. Ryabinin

Addresses: N.G. Kuznetsov Naval Academy, Ushakovskaya naberezhnaya, 17/1, Sankt-Petersburg, Russia

Abstract: Finding analogies between the mathematical logic and the probability theory is both of theoretical and practical importance. George Boole in An Investigation of the Laws of Thought, On Which are Founded the Mathematical Theories of Logic and Probabilities published in London in 1854 expressed a far-sighted idea on applicability of the mathematical logic to the probability theory. It is therefore astonishing, that during the last one and a half centuries not a single mathematician expressed his/her opinion on this matter, which gave reason to critics who said there is no mention on any relation between this science and the algebra of logic in any large publications on the probability theory, in particular, in publications of such academicians as A.A. Markov, A.N. Kolmogorov, etc. What is a phenomenon of the logical probabilistic analysis and why it is neglected by mathematicians?

Keywords: mathematical logic; probability theory; probabilistic analysis; logical function; orthogonalisation algorithm; Boolean algebra; probabilistic function; events; logical equations.

DOI: 10.1504/IJRAM.2015.071213

International Journal of Risk Assessment and Management, 2015 Vol.18 No.3/4, pp.256 - 265

Received: 19 Apr 2014
Accepted: 03 Oct 2014

Published online: 17 Aug 2015 *

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