Probability Logics. Probability-Based Formalization of Uncertain Reasoning

Abstract

This introduction gives an overview of some fields of mathematical logic and underlying principles (ω-rule, Lω1ω, nonstandard analysis, admissible sets, modal logics) that are used in the rest of the book. Particularly, it provides motivation for various applications of infinitary means in obtaining the presented results. A comparison between the mainstream approach to mathematical theory of probability based on Kolmogorov’s axioms and probability logics is given. Finally, the organization of the book is presented.