Equational Coalgebraic Logic

Authors

Alexander Kurz, Chapman UniversityFollow
Raul Leal, Universiteit van Amsterdam

Document Type

Article

Publication Date

2009

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.

Comments

This article was originally published in Electronic Notes in Theoretical Computer Science, volume 249, in 2009. DOI: 10.1016/j.entcs.2009.07.097

Recommended Citation

A. Kurz and R. Leal, “Equational Coalgebraic Logic,” Electronic Notes in Theoretical Computer Science, vol. 249, pp. 333–356, Aug. 2009. DOI: 10.1016/j.entcs.2009.07.097

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.