Riesz modal logic for Markov processes

Matteo Mio; Robert Furber; Radu Mardare

doi:10.1109/LICS.2017.8005091

Riesz modal logic for Markov processes

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

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.

Original language	English
Title of host publication	32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Publisher	IEEE
ISBN (Electronic)	9781509030187
DOIs	https://doi.org/10.1109/LICS.2017.8005091
Publication status	Published - 10 Aug 2017
Event	32nd Annual ACM/IEEE Symposium on Logic in Computer Science 2017 - Reykjavik, Iceland Duration: 20 Jun 2017 → 23 Jun 2017

Conference

Conference	32nd Annual ACM/IEEE Symposium on Logic in Computer Science 2017
Abbreviated title	LICS 2017
Country/Territory	Iceland
City	Reykjavik
Period	20/06/17 → 23/06/17

Keywords

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

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10.1109/LICS.2017.8005091

https://www.scopus.com/pages/publications/85034112812

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@inproceedings{8c8338579ea644af99aa3b03cb6d1fc1,

title = "Riesz modal logic for Markov processes",

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.",

keywords = "Markov processes, Radon, extraterrestrial measurements, calculus, topology, probabilistic logics, algebra, category theory, duality (mathematics), formal logic",

author = "Matteo Mio and Robert Furber and Radu Mardare",

year = "2017",

month = aug,

day = "10",

doi = "10.1109/LICS.2017.8005091",

language = "English",

booktitle = "32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)",

publisher = "IEEE",

address = "United States",

note = "32nd Annual ACM/IEEE Symposium on Logic in Computer Science 2017, LICS 2017 ; Conference date: 20-06-2017 Through 23-06-2017",

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T1 - Riesz modal logic for Markov processes

AU - Mio, Matteo

AU - Furber, Robert

AU - Mardare, Radu

PY - 2017/8/10

Y1 - 2017/8/10

N2 - 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.

AB - 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.

KW - Markov processes

KW - Radon

KW - extraterrestrial measurements

KW - calculus

KW - topology

KW - probabilistic logics

KW - algebra

KW - category theory

KW - duality (mathematics)

KW - formal logic

U2 - 10.1109/LICS.2017.8005091

DO - 10.1109/LICS.2017.8005091

M3 - Conference contribution

BT - 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

PB - IEEE

T2 - 32nd Annual ACM/IEEE Symposium on Logic in Computer Science 2017

Y2 - 20 June 2017 through 23 June 2017

ER -

Riesz modal logic for Markov processes

Abstract

Conference

Keywords

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