Modal Predicates and Coequations

Authors

Alexander Kurz, Chapman UniversityFollow
Jiří Rosický, Masaryk University

Document Type

Article

Publication Date

2002

Abstract

We show how coalgebras can be presented by operations and equations. This is a special case of Linton’s approach to algebras over a general base category X, namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.

Comments

This article was originally published in Electronic Notes in Theoretical Computer Science, volume 65, number 1, in 2002. DOI: 10.1016/S1571-0661(04)80364-5

Recommended Citation

A. Kurz and J. Rosický, “Modal Predicates and Coequations,” Electronic Notes in Theoretical Computer Science, vol. 65, no. 1, pp. 156–175, Oct. 2002. DOI: 10.1016/S1571-0661(04)80364-5

Copyright

Elsevier

Creative Commons License

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