Stone duality for markov processes

Dexter Kozen; Kim G. Larsen; Radu Mardare; Prakash Panangaden

doi:10.1109/LICS.2013.38

Stone duality for markov processes

Dexter Kozen, Kim G. Larsen, Radu Mardare, Prakash Panangaden

Research output: Contribution to journal › Conference article › peer-review

19 Citations (Scopus)

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.

Original language	English
Article number	6571564
Pages (from-to)	321-330
Number of pages	10
Journal	Proceedings - Symposium on Logic in Computer Science
Early online date	1 Aug 2013
DOIs	https://doi.org/10.1109/LICS.2013.38
Publication status	Published - 9 Sept 2013
Event	2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013 - New Orleans, LA, United States Duration: 25 Jun 2013 → 28 Jun 2013

Keywords

completeness
labelled Markov processes
probabilistic modal logics
tone-type duality

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10.1109/LICS.2013.38

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AB - 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.

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KW - labelled Markov processes

KW - probabilistic modal logics

KW - tone-type duality

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ER -

Stone duality for markov processes

Abstract

Keywords

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