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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... (Update)
Context of citations to this paper: More
.... in the 1940 s (information supplied by Paul Cohn and Bernhard Neumann) 15 functors, and extended to polynomial functors in [14, 13]. It involves a new notion of ultra lter enlargement of a coalgebra, an analogue of the Stone space of a Boolean algebra. These ideas can...
.... of work centred around the mentioned duality, especially to establish coalgebraic versions of Birkho s variety theorem, see e.g. 6] 2] [1]. It is commonly seen as one of the biggest advantages of coalgebras that they deliver standard notions like bisimulation, observational...
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4: A Co-variety-theorem for modal logic (context) - Kurz - 1998
3: An Approach to Object Semantics based on Terminal Co-algebras (context) - Reichel - 1995
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BibTeX entry: (Update)
Robert Goldblatt. A calculus of terms for coalgebras of polynomial functors. Electronic Notes in Theoretical Computer Science, 44, Issue 1, 2001. http://www.elsevier.nl/ locate/entcs. http://citeseer.ist.psu.edu/goldblatt01calculus.html More
@misc{ goldblatt01calculus,
author = "R. Goldblatt",
title = "A calculus of terms for coalgebras of polynomial functors",
text = "Robert Goldblatt. A calculus of terms for coalgebras of polynomial functors.
Electronic Notes in Theoretical Computer Science, 44, Issue 1, 2001. http://www.elsevier.nl/
locate/entcs.",
year = "2001",
url = "citeseer.ist.psu.edu/goldblatt01calculus.html" }
Citations (may not include all citations):227 North-Holland (context) - Chang, Keisler - 1973
186 Universal Coalgebra: a Theory of Systems - Rutten - 2000
121 An Approach to Object Semantics Based on Terminal Co-Algebra.. (context) - Reichel - 1995
91 A Final Coalgebra Theorem (context) - Aczel, Mendler
72 Objects and Classes (context) - Jacobs - 1996
38 Categorical Logic and Type Theory (context) - Jacobs - 1999
36 Categorical Logic - Pitts - 2000
33 Annals of Pure and Applied Logic (context) - Moss - 1999
30 Specifying Coalgebras with Modal Logic (context) - Kurz - 1998
20 towards Universal Coalgebra (context) - Rutten, of - 1995
18 Models and Ultraproducts (context) - Bell, Slomson - 1969
17 Structural induction and coinduction in a brational setting (context) - Hermida, Jacobs - 1998
12 Also available as Aarhus Univ (context) - Hermida, Fibrations et al. - 1993
10 Towards a Duality Result in Coalgebraic Modal Logic (context) - Jacobs - 2000
8 From Modal Logic to Terminal Coalgebras (context) - iger
3 manuscript for the proceedings of the Mathematics for Inform.. (context) - Jacobs - 2000
http://www.mcs.vuw.ac.nz/~rob/papers/what.ps
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