Final coalgebras and the Hennessy-Milner property Export

@article{citeulike:565331, abstract = {The existence of a final coalgebra is equivalent to the existence of a formal logic with a set (small class) of formulas that has the Hennessy-Milner property of distinguishing coalgebraic states up to bisimilarity. This applies to coalgebras of any functor on the category of sets for which the bisimilarity relation is transitive. There are cases of functors that do have logics with the Hennessy-Milner property, but the only such logics have a proper class of formulas.The main theorem gives a representation of states of the final coalgebra as certain satisfiable sets of formulas. The key technical fact used is that any function between coalgebras that is truth-preserving and has a simple codomain must be a coalgebraic morphism.}, author = {Goldblatt, Robert}, booktitle = {New Zealand Institute of Mathematics and its Applications: Logic and Computation Programme}, citeulike-article-id = {565331}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.apal.2005.06.006}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6TYB-4GKW6Y2-3/2/ca5617550001570aa992d8dc38c42538}, doi = {10.1016/j.apal.2005.06.006}, journal = {Annals of Pure and Applied Logic}, keywords = {abstract\_logic, bisimilarity, bisimulation, coalgebra, coinductive, congruence, final\_object}, month = {March}, number = {1-3}, pages = {77--93}, posted-at = {2006-03-27 11:42:14}, priority = {0}, title = {Final coalgebras and the Hennessy-Milner property}, url = {http://dx.doi.org/10.1016/j.apal.2005.06.006}, volume = {138}, year = {2006} }

TY - JOUR ID - citeulike:565331 L3 - citeulike-article-id:565331 N2 - The existence of a final coalgebra is equivalent to the existence of a formal logic with a set (small class) of formulas that has the Hennessy-Milner property of distinguishing coalgebraic states up to bisimilarity. This applies to coalgebras of any functor on the category of sets for which the bisimilarity relation is transitive. There are cases of functors that do have logics with the Hennessy-Milner property, but the only such logics have a proper class of formulas.The main theorem gives a representation of states of the final coalgebra as certain satisfiable sets of formulas. The key technical fact used is that any function between coalgebras that is truth-preserving and has a simple codomain must be a coalgebraic morphism. IS - 1-3 JF - Annals of Pure and Applied Logic EP - 93 TI - Final coalgebras and the Hennessy-Milner property VL - 138 T2 - New Zealand Institute of Mathematics and its Applications: Logic and Computation Programme SP - 77 KW - abstract_logic KW - bisimilarity KW - bisimulation KW - coalgebra KW - coinductive KW - congruence KW - final_object AU - Goldblatt, Robert PY - 2006/03// UR - http://dx.doi.org/10.1016/j.apal.2005.06.006 ER -