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  1.  2 DLs
    Ernst-Erich Doberkat (2012). A Stochastic Interpretation of Propositional Dynamic Logic: Expressivity. Journal of Symbolic Logic 77 (2):687-716.
    We propose a probabilistic interpretation of Propositional Dynamic Logic (PDL). We show that logical and behavioral equivalence are equivalent over general measurable spaces. This is done first for the fragment of straight line programs and then extended to cater for the nondeterministic nature of choice and iteration, expanded to PDL as a whole. Bisimilarity is also discussed and shown to be equivalent to logical and behavioral equivalence, provided the base spaces are Polish spaces. We adapt techniques from coalgebraic stochastic logic (...)
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  2.  1 DLs
    Ernst-Erich Doberkat (2012). Lattice Properties of Congruences for Stochastic Relations. Annals of Pure and Applied Logic 163 (8):1016-1029.
  3.  1 DLs
    Ernst-Erich Doberkat & Christoph Schubert (2009). Coalgebraic Logic for Stochastic Right Coalgebras. Annals of Pure and Applied Logic 159 (3):268-284.
    We generalize stochastic Kripke models and Markov transition systems to stochastic right coalgebras. These are coalgebras for a functor with as an endofunctor on the category of analytic spaces, and is the subprobability functor. The modal operators are generalized through predicate liftings which are set-valued natural transformations involving the functor. Two states are equivalent iff they cannot be separated by a formula. This equivalence relation is used to construct a cospan for logical equivalent coalgebras under a separation condition for the (...)
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    Ernst-Erich Doberkat (2008). Stochastic Coalgebraic Logic: Bisimilarity and Behavioral Equivalence. Annals of Pure and Applied Logic 155 (1):46-68.
    Bisimulations, behavioral equivalence and logical equivalence are investigated for stochastic image-coalgebras that interpret coalgebraic logic which is defined in terms of predicate liftings. We investigate the conditions for the functor under which these notions of equivalence are related by discussing congruences for the underlying stochastic relation. It is demonstrated that logics as diverse as continuous time stochastic logic and general modal logics can be usefully approached through coalgebraic methods.
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