TY - JOUR

T1 - Coalgebras and modal expansions of logics

AU - Kurz, Alexander

AU - Palmigiano, Alessandra

PY - 2004/12/12

Y1 - 2004/12/12

N2 - 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)).

AB - 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)).

KW - Coalgebra

KW - Modal expansion

KW - Modal logic

KW - Stone space

KW - Vietoris endofunctor

UR - http://www.scopus.com/inward/record.url?scp=10444247372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10444247372&partnerID=8YFLogxK

U2 - 10.1016/j.entcs.2004.05.010

DO - 10.1016/j.entcs.2004.05.010

M3 - Article

AN - SCOPUS:10444247372

VL - 107

SP - 243

EP - 259

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

SN - 1571-0661

IS - 1-4 SPEC. ISS.

ER -