Probability Logic: A Model Theoretic Perspective

Por • 1 nov, 2018 • Sección: Ambiente

Massoud Pourmahdian, Reihane Zoghifard

In this paper (propositional) probability logic (PL) 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 PL called basic probability logic (BPL). 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 (PPL). We finally prove that while the Lowenheim-Skolem number of the class of σ-additive probability models is uncountable, it is ℵ0 for the class of finitely additive probability models.

arXiv:1810.07413v1 [math.LO]

Logic (math.LO)

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