Stone Duality for Markov Processes
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Kozen, Dexter; Larsen, Kim G.; Mardare, Radu; Panangaden, Prakash
We define Aumann algebras, an algebraic analog of probabilistic modal logic. An Aumann algebra consists of a Boolean algebra with operators modeling probabilistic transitions. We prove that countable Aumann algebras and countably-generated continuous-space Markov processes are dual in the sense of Stone. Our results subsume existing results on completeness of probabilistic modal logics for Markov processes.
Stone duality; Aumann algebra; Markov process; probabilistic logic