| Autor: |
Marta Bílková, Matěj Dostál |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Logical Methods in Computer Science, Vol Volume 18, Issue 3 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
1860-5974 |
| DOI: |
10.46298/lmcs-18(3:18)2022 |
| Popis: |
We present a finitary version of Moss' coalgebraic logic for $T$-coalgebras, where $T$ is a locally monotone endofunctor of the category of posets and monotone maps. The logic uses a single cover modality whose arity is given by the least finitary subfunctor of the dual of the coalgebra functor $T_\omega^\partial$, and the semantics of the modality is given by relation lifting. For the semantics to work, $T$ is required to preserve exact squares. For the finitary setting to work, $T_\omega^\partial$ is required to preserve finite intersections. We develop a notion of a base for subobjects of $T_\omega X$. This in particular allows us to talk about the finite poset of subformulas for a given formula. The notion of a base is introduced generally for a category equipped with a suitable factorisation system. We prove that the resulting logic has the Hennessy-Milner property for the notion of similarity based on the notion of relation lifting. We define a sequent proof system for the logic, and prove its completeness. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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