A Calculus of Terms for Coalgebras of Polynomial Functors Export

@article{citeulike:565334, abstract = {A syntax and semantics of types, terms and formulas for coalgebras of polynomial functors is developed, extending earlier work [4] on monomial coalgebras to include functors constructed using coproducts. A modified ultrapower construction for polynomial coalgebras is introduced, adapting the conventional ultrapower to retain only those states that evaluate observable terms in a standard way.A special role is played by terms that take observable values and are \“rigid\”: their free variables do not occur in any state-valued subterm. The following \“co-Birkhoff\” theorem is proved: a class of polynomial coalgebras is definable by Boolean combinations of equations between rigid terms iff the class is closed under disjoint unions, images of bisimulations, and observable ultrapowers.}, author = {Goldblatt, Robert}, booktitle = {CMCS 2001, Coalgebraic Methods in Computer Science (a Satellite Event of ETAPS 2001)}, citeulike-article-id = {565334}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/S1571-0661(04)80907-1}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B75H1-4DDWHYH-2S/2/2cda78d80852f1600c5cb2b7e3f72d1c}, doi = {10.1016/S1571-0661(04)80907-1}, journal = {Electronic Notes in Theoretical Computer Science}, keywords = {coalgebra, polynomial\_functor}, month = {May}, number = {1}, pages = {1--24}, posted-at = {2006-03-27 11:50:26}, priority = {0}, title = {A Calculus of Terms for Coalgebras of Polynomial Functors}, url = {http://dx.doi.org/10.1016/S1571-0661(04)80907-1}, volume = {44}, year = {2001} }

TY - JOUR ID - citeulike:565334 L3 - citeulike-article-id:565334 N2 - A syntax and semantics of types, terms and formulas for coalgebras of polynomial functors is developed, extending earlier work [4] on monomial coalgebras to include functors constructed using coproducts. A modified ultrapower construction for polynomial coalgebras is introduced, adapting the conventional ultrapower to retain only those states that evaluate observable terms in a standard way.A special role is played by terms that take observable values and are “rigid”: their free variables do not occur in any state-valued subterm. The following “co-Birkhoff” theorem is proved: a class of polynomial coalgebras is definable by Boolean combinations of equations between rigid terms iff the class is closed under disjoint unions, images of bisimulations, and observable ultrapowers. IS - 1 JF - Electronic Notes in Theoretical Computer Science EP - 24 TI - A Calculus of Terms for Coalgebras of Polynomial Functors VL - 44 T2 - CMCS 2001, Coalgebraic Methods in Computer Science (a Satellite Event of ETAPS 2001) SP - 1 KW - coalgebra KW - polynomial_functor AU - Goldblatt, Robert PY - 2001/05// UR - http://dx.doi.org/10.1016/S1571-0661(04)80907-1 ER -