中文

Goldblatt-Thomason Theorem for Probability Logic

计算机科学中的逻辑 2026-06-30 v1

摘要

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 (Ω,Σ,T)(\Omega, \Sigma, T), where(Ω,Σ)(\Omega, \Sigma) is a measurable space and TT 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.

引用

@article{arxiv.2606.31865,
  title  = {Goldblatt-Thomason Theorem for Probability Logic},
  author = {Somayeh Chopoghloo and Massoud Pourmahdian and Reihane Zoghifard},
  journal= {arXiv preprint arXiv:2606.31865},
  year   = {2026}
}

备注

In Proceedings AiML 2026, arXiv:2606.29444