Stone Duality for Markov Processes

Authors:
Dexter Kozen;Kim G. Larsen;Radu Mardare;Prakash Panangaden
Affiliations:
-;-;-;-
Venue:
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
Year:
2013

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Abstract

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 a Stone-type duality between countable Aumann algebras and countably-generated continuous-space Markov processes. Our results subsume existing results on completeness of probabilistic modal logics for Markov processes.