| Autor: |
Sebastian Enqvist, Fatemeh Seifan, Yde Venema |
| Jazyk: |
angličtina |
| Rok vydání: |
2017 |
| Předmět: |
|
| Zdroj: |
Logical Methods in Computer Science, Vol Volume 13, Issue 2 (2017) |
| Druh dokumentu: |
article |
| ISSN: |
1860-5974 |
| DOI: |
10.23638/LMCS-13(2:14)2017 |
| Popis: |
Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas. More specifically, we investigate whether the coalgebraic mu-calculus is the bisimulation-invariant fragment of the monadic second-order language for a given functor. Using automatatheoretic techniques and building on recent results by the third author, we show that in order to provide such a characterization result it suffices to find what we call an adequate uniform construction for the coalgebraic type functor. As direct applications of this result we obtain a partly new proof of the Janin-Walukiewicz Theorem for the modal mu-calculus, avoiding the use of syntactic normal forms, and bisimulation invariance results for the bag functor (graded modal logic) and all exponential polynomial functors (including the "game functor"). As a more involved application, involving additional non-trivial ideas, we also derive a characterization theorem for the monotone modal mu-calculus, with respect to a natural monadic second-order language for monotone neighborhood models. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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