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
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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 -