Stone Duality for Markov Processes

Author

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

Author_Institution

Comput. Sci. Dept., Cornell Univ., Ithaca, NY, USA

fYear

2013

fDate

25-28 June 2013

Firstpage

321

Lastpage

330

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 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.

Keywords

Boolean algebra; Markov processes; duality (mathematics); formal logic; probability; Boolean algebra; algebraic analog; countable Aumann algebra; countably-generated continuous-space Markov processes; probabilistic modal logics completeness; probabilistic transition modeling; stone duality; stone-type duality theorem; Boolean algebra; Computer science; Extraterrestrial measurements; Markov processes; Probabilistic logic; Topology; Labelled Markov processes; Probabilistic modal logics; Stone-type duality; completeness;

fLanguage

English

Publisher

ieee

Conference_Titel

Logic in Computer Science (LICS), 2013 28th Annual IEEE/ACM Symposium on

Conference_Location

New Orleans, LA

ISSN

1043-6871

Print_ISBN

978-1-4799-0413-6

Type

conf

DOI

10.1109/LICS.2013.38

Filename

6571564

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=626299