Abstract
The relationship between congruences and bisimulations is investigated for stochastic relations. It is shown that stochastic relations are bisimilar provided they have congruences that generate each other; from this is derived that relations that have isomorphic factor spaces are bisimilar. Stochastic Kripke models are introduced for a modal logic and illustrated for some popular logics. The criterion developed here permits proving for the general case that Kripke models are bisimilar iff they accept exactly the same formulas.
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