Coalgebras and modal expansions of logics

Alexander Kurz*, Alessandra Palmigiano

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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, double-struck A sign), ie sets X equipped with an algebra double-struck A sign of subsets of X, allows for the definition of powerspaces V (and hence transition systems (X, double-struck A sign) → V(X, double-struck A sign)).

Original languageEnglish
Pages (from-to)243-259
Number of pages17
JournalElectronic Notes in Theoretical Computer Science
Volume107
Issue number1-4 SPEC. ISS.
DOIs
Publication statusPublished - 12 Dec 2004
Externally publishedYes

Keywords

  • Coalgebra
  • Modal expansion
  • Modal logic
  • Stone space
  • Vietoris endofunctor

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