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 |
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| 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/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
