Doberkat, Ernst-Erich2004-12-062004-12-0620032004-05-12http://hdl.handle.net/2003/272310.17877/DE290R-5187We discuss congruences for stochastic relations, stressing the equivalence of smooth equivalence relations and countably generated ó-algebras. Factor spaces are constructed for congruences and for morphisms. Semi-pullbacks are needed when investigating the interplay between congruences and bisimulations, and it is shown that semi-pullbacks exist for stochastic relations over analytic spaces, generalizing a previous result and answering an open question. Equivalent congruences are investigated, and it is shown that stochastic relations that have equivalent congruences are bisimilar. The well-known equivalence relation coming from a Hennessy-Milner logic for labelled Markov transition systems is shown to be a special case in this development.enUniversität Dortmundbisimulationcongruencesfactorizationsemi-pullbacksStochastic relations over Polish and analytic spaces004working paper