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Equational Coalgebraic Logic (2009)
| Venue: | MFPS |
| Citations: | 7 - 2 self |
BibTeX
@MISC{Kurz09equationalcoalgebraic,
author = {Alexander Kurz and Raul Leal},
title = {Equational Coalgebraic Logic},
year = {2009}
}
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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 [21] 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.
Keyphrases
equational coalgebraic logic stone duality restricted class generic logic general theory possible one-step behaviour transition system one-step translation novel coalgebraic logic general case coalgebraic logic arbitrary functor fundamental question predicate liftings moss logic equational axiomatization main contribution systematic use
