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Quantifying over events in probability logic: an introduction

Published online by Cambridge University Press:  29 June 2016

STANISLAV O. SPERANSKI
STANISLAV O. SPERANSKI*
Affiliation:
Sobolev Institute of Mathematics, 4 Koptyug ave., 630090 Novosibirsk, Russia Email: katze.tail@gmail.com
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Abstract

In this article we describe a bunch of probability logics with quantifiers over events, and develop primary techniques for proving computational complexity results (in terms of m-degrees) about these logics, mainly over discrete probability spaces. Also the article contains a comparison with some other probability logics and a discussion of interesting analogies with research in the metamathematics of Boolean algebras, demonstrating a number of attractive features and intuitive advantages of the present proposal.

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