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