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arXiv · 2606.31865

Goldblatt-Thomason Theorem for Probability Logic

Somayeh Chopoghloo·Massoud Pourmahdian·Reihane Zoghifard
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Abstract

Probability logic (PL) extends propositional logic with countably many probability operators, one for each rational number between 0 and 1. The formulas of this logic are interpreted over the class of Markov processes, i.e., structures of the form $(\Omega, \Sigma, T)$, where$(\Omega, \Sigma)$ is a measurable space and $T$ is a Markov kernel. The main contribution of this paper is the establishment of the Goldblatt-Thomason theorem for probability logic. As an application, we show that the class of Harsanyi type spaces is definable in PL. Moreover, we obtain some variants of the Goldblatt-Thomason theorem for specific subclasses of Markov processes.

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Somayeh Chopoghloo, Massoud Pourmahdian, Reihane Zoghifard. 2026-06-30. Goldblatt-Thomason Theorem for Probability Logic. https://doi.org/10.4204/eptcs.447.12

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