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: Chapter in Book/Report/Conference proceeding › Conference contribution

20 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
Title of host publication	Proceedings of the 28th Annual ACM/IEEE Symposium on Logic in Computer Science
Pages	321-330
Number of pages	10
DOIs	https://doi.org/10.1109/LICS.2013.38
Publication status	Published - 2013
Event	28th Annual ACM/IEEE Symposium on Logic in Computer Science - New Orleans, United States Duration: 25 Jun 2013 → 28 Jun 2013

Conference

Conference	28th Annual ACM/IEEE Symposium on Logic in Computer Science
Abbreviated title	LIC 2013
Country/Territory	United States
City	New Orleans
Period	25/06/13 → 28/06/13

Keywords

completeness
labelled Markov processes
probabilistic modal logics
tone-type duality

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10.1109/LICS.2013.38

https://www.scopus.com/pages/publications/84883362276

Cite this

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title = "Stone duality for Markov processes",

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.",

keywords = "completeness, labelled Markov processes, probabilistic modal logics, tone-type duality",

author = "Dexter Kozen and Larsen, \{Kim G.\} and Radu Mardare and Prakash Panangaden",

note = "M1 - 6571564; 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LIC 2013 ; Conference date: 25-06-2013 Through 28-06-2013",

year = "2013",

doi = "10.1109/LICS.2013.38",

language = "English",

isbn = "978-1-4799-0413-6",

pages = "321--330",

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AU - Kozen, Dexter

AU - Larsen, Kim G.

AU - Mardare, Radu

AU - Panangaden, Prakash

N1 - M1 - 6571564

PY - 2013

Y1 - 2013

N2 - 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.

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.

KW - completeness

KW - labelled Markov processes

KW - probabilistic modal logics

KW - tone-type duality

U2 - 10.1109/LICS.2013.38

DO - 10.1109/LICS.2013.38

M3 - Conference contribution

SN - 978-1-4799-0413-6

SP - 321

EP - 330

BT - Proceedings of the 28th Annual ACM/IEEE Symposium on Logic in Computer Science

T2 - 28th Annual ACM/IEEE Symposium on Logic in Computer Science

Y2 - 25 June 2013 through 28 June 2013

ER -

Stone duality for Markov processes

Abstract

Conference

Keywords

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