Stone Duality for Markov Processes

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 theorem between countable Aumann algebras and countably-generated continuous-space Markov proc...

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Vydáno v:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science s. 321 - 330
Hlavní autoři: Kozen, Dexter, Larsen, Kim G., Mardare, Radu, Panangaden, Prakash
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.06.2013
Témata:
Boolean algebra
completeness
Computer science
Extraterrestrial measurements
Labelled Markov processes
Markov processes
Probabilistic logic
Probabilistic modal logics
Stone-type duality
Topology
ISBN:1479904139, 9781479904136
ISSN:1043-6871
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Popis
Shrnutí: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 theorem 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.
ISBN:1479904139
9781479904136
ISSN:1043-6871
DOI:10.1109/LICS.2013.38