Hyperfinite Approximations to Labeled Markov Transition Systems

The problem of finding an approximation to a labeled Markov transition system through hyperfinite transition systems is addressed. It is shown that we can find for each countable family of stochastic relations on Polish spaces a family of relations defined on a hyperfinite set that is infinitely close. This is applied to Kripke models for a simple modal logic in the tradition of Larsen and Skou. It follows that we can find for each Kripke model a hyperfinite one which is infinitely close.

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