Document Type
Article
Publication Date
2004
Abstract
In this paper we construct a setting in which the question of when a logic supports a classical modal expansion can be made precise. Given a fully selfextensional logic S, we find sufficient conditions under which the Vietoris endofunctor V on S-referential algebras can be defined and we propose to define the modal expansions of S as the logic that arises from the V-coalgebras. As an example, we also show how the Vietoris endofunctor on referential algebras extends the Vietoris endofunctor on Stone spaces. From another point of view, we examine when a category of ‘spaces’ (X,A), ie sets X equipped with an algebra A of subsets of X, allows for the definition of powerspaces V (and hence transition systems (X,A) → V(X,A)).
Recommended Citation
A. Kurz and A. Palmigiano, “Coalgebras and Modal Expansions of Logics,” Electronic Notes in Theoretical Computer Science, vol. 106, pp. 243–259, Dec. 2004. DOI: 10.1016/j.entcs.2004.05.010
Copyright
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Included in
Algebra Commons, Logic and Foundations Commons, Other Computer Engineering Commons, Other Computer Sciences Commons, Other Mathematics Commons
Comments
This article was originally published in Electronic Notes in Theoretical Computer Science, volume 106, in 2004. DOI: 10.1016/j.entcs.2004.05.010