PP-2009-16: Leal, Raul and Kurz, Alexander (2009) Equational Coalgebraic Logic. [Report]
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Abstract
Coalgebra develops a general theory of transition systems,
parametric in a functor $T$; the functor $T$ specifies the possible
one-step behaviours of the system. A fundamental question in this
area is how to obtain, for an arbitrary functor $T$, a logic for
$T$-coalgebras. We compare two existing proposals, Moss's
coalgebraic logic and the logic of all predicate liftings, by
providing one-step translations between them, extending the results
in \cite{leal:cmcs08} by making systematic use of Stone duality. Our
main contribution then is a novel coalgebraic logic, which can be
seen as an equational axiomatization of Moss's logic. The three
logics are equivalent for a natural but restricted class of
functors. We give examples showing that the logics fall apart in
general. Finally, we argue that the quest for a generic logic for
$T$-coalgebras is still open in the general case.
| Item Type: | Report |
|---|---|
| Report Nr: | PP-2009-16 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2009 |
| Uncontrolled Keywords: | Coalgebra; Caolgebraic Logic; Stone Duality; Predicate liftings; Moss' modality |
| Depositing User: | raulleal |
| Date Deposited: | 12 Oct 2016 14:37 |
| Last Modified: | 12 Oct 2016 14:37 |
| URI: | https://eprints.illc.uva.nl/id/eprint/346 |
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