Behavioral and Logical Equivalence of Stochastic Kripke Models in General Measurable Spaces

Abstract

We show that logical and behavioral equivalence for stochastic Kripke models over general measurable spaces are the same. Usually, this requires some topological assumptions and includes bisimilarity; the results here indicate that a measurable structure on the state space of the Kripke model suffices. In contrast to a paper by Danos et al. we focus on the measurable structure of the factor space induced by the logic. This technique worked well in the analytic case, and it is shown to work here as well. The main contribution of the paper is methodological, since it provides a uniform framework for general measurable as well as more specialized analytic spaces.