### 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.

Language | English |
---|---|

Title of host publication | 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 |

Number of pages | 12 |

ISBN (Electronic) | 9781509030187 |

DOIs | |

Publication status | Published - 8 Aug 2017 |

Event | 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 - Reykjavik, Iceland Duration: 20 Jun 2017 → 23 Jun 2017 |

### Conference

Conference | 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 |
---|---|

Country | Iceland |

City | Reykjavik |

Period | 20/06/17 → 23/06/17 |

### Fingerprint

### Keywords

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

### Cite this

*32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017*[8005091] https://doi.org/10.1109/LICS.2017.8005091

}

*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.

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

TY - GEN

T1 - Riesz modal logic for Markov processes

AU - Mio, Matteo

AU - Furber, Robert

AU - Mardare, Radu

PY - 2017/8/8

Y1 - 2017/8/8

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

UR - http://www.scopus.com/inward/record.url?scp=85034112812&partnerID=8YFLogxK

U2 - 10.1109/LICS.2017.8005091

DO - 10.1109/LICS.2017.8005091

M3 - Conference contribution book

BT - 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017

ER -