Riesz modal logic for Markov processes

Matteo Mio, Robert Furber, Radu Mardare

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

2 Citations (Scopus)

Abstract

We investigate a modal logic for expressing properties of Markov processes whose semantics is real-valued, rather than Boolean, and based on the mathematical theory of Riesz spaces. We use the duality theory of Riesz spaces to provide a connection between Markov processes and the logic. This takes the form of a duality between the category of coalgebras of the Radon monad (modeling Markov processes) and the category of a new class of algebras (algebraizing the logic) which we call modal Riesz spaces. As a result, we obtain a sound and complete axiomatization of the Riesz Modal logic.

LanguageEnglish
Title of host publication32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
Number of pages12
ISBN (Electronic)9781509030187
DOIs
Publication statusPublished - 8 Aug 2017
Event32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 - Reykjavik, Iceland
Duration: 20 Jun 201723 Jun 2017

Conference

Conference32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
CountryIceland
CityReykjavik
Period20/06/1723/06/17

Fingerprint

Riesz Space
Modal Logic
Markov Process
Markov processes
Logic
Monads
Duality Theory
Coalgebra
Radon
Axiomatization
Duality
Semantics
Acoustic waves
Modeling

Keywords

  • Markov processes
  • Radon
  • extraterrestrial measurements
  • calculus
  • topology
  • probabilistic logics
  • algebra
  • category theory
  • duality (mathematics)
  • formal logic

Cite this

Mio, M., Furber, R., & Mardare, R. (2017). Riesz modal logic for Markov processes. In 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 [8005091] https://doi.org/10.1109/LICS.2017.8005091
Mio, Matteo ; Furber, Robert ; Mardare, Radu. / Riesz modal logic for Markov processes. 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017. 2017.
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Mio, M, Furber, R & Mardare, R 2017, Riesz modal logic for Markov processes. in 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017., 8005091, 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017, Reykjavik, Iceland, 20/06/17. https://doi.org/10.1109/LICS.2017.8005091

Riesz modal logic for Markov processes. / Mio, Matteo; Furber, Robert; Mardare, Radu.

32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017. 2017. 8005091.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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Mio M, Furber R, Mardare R. Riesz modal logic for Markov processes. In 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017. 2017. 8005091 https://doi.org/10.1109/LICS.2017.8005091