Probability Logic: A Model Theoretic Perspective

Abstract

In this paper (propositional) probability logic (P L) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for σ-additive probability models, and subsequently when this class of models is considered it is shown that the compactness property holds with respect to a fragment of P L called basic probability logic (BP L). On the other hand, when dealing with finitely-additive probability models, one may extend the compactness property for a larger fragment of probability logic, namely positive probability logic (P P L). We finally prove that while the Löwenheim-Skolem number of the class of σ-additive probability models is uncountable, it is ℵ 0 for the class of finitely additive probability models.