Abstract
A logic for coalgebras is said to admit final semantics iff— up to some technical requirements—all definable classes contain a fully abstract final coalgebra. It is shown that a logic admits final semantics iff the formulas of the logic are preserved under coproducts (disjoint unions) and quotients (homomorphicimages).
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References
S. Awodey and J. Hughes. The coalgebraic dual of Birkhoff’s variety theorem. Technical Report CMU-PHIL-109, Carnegie Mellon University, Pittsburgh, PA, 15213, November 2000.
P. Blackburn, M. de Rijke, and Y. Venema. Modal Logic. Cambridge University Press, 2001. See also http://www.mlbook.org.
A. Corradini, M. Lenisa, and U. Montanari, editors. Coalgebraic Methods in Computer Science (CMCS’01), volume 44–1 of Electronic Notes in Theoretical Computer Science, 2001.
Robert Goldblatt. A calculus of terms for coalgebras of polynomial functors. In A. Corradini, M. Lenisa, and U. Montanari, editors, Coalgebraic Methods in Computer Science (CMCS’01), volume 44.1 of ENTCS. Elsevier, 2001.
H. P. Gumm and T. Schröder. Covarieties and complete covarieties. Theoretical Computer Science, 260:71–86, 2001.
B. Jacobs, L. Moss, H. Reichel, and J. Rutten, editors. Coalgebraic Methods in Computer Science (CMCS’98), volume 11. Electronic Notes in Theoretical Computer Science, 1998.
B. Jacobs and J. Rutten. A tutorial on (co)algebras and (co)induction. EATCS Bulletin, 62, 1997.
B. Jacobs and J. Rutten, editors. Coalgebraic Methods in Computer Science, volume 19. Electronic Notes in Theoretical Computer Science, 1999.
Bart Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83–103. Kluwer Acad. Publ., 1996.
Bart Jacobs. Many-sorted coalgebraic modal logic: a model-theoretic study. Theoretical Informatics and Applications, 35(1):31–59, 2001.
A. Kurz and D. Pattinson. Coalgebras and modal logics for parameterised endofunctors. Technical Report SEN-R0040, CWI, 2000. http://www.cwi.nl/~kurz.
Alexander Kurz. A co-variety-theorem for modal logic. In Advances in Modal Logic 2. Center for the Study of Language and Information, Stanford University, 2001.
Alexander Kurz. Modal rules are co-implications. In A. Corradini, M. Lenisa, and U. Montanari, editors, Coalgebraic Methods in Computer Science (CMCS’01), volume 44.1 of ENTCS. Elsevier, 2001.
Alexander Kurz. Specifying coalgebras with modal logic. Theoretical Computer Science, 260:119–138, 2001.
B. Mahr and J. A. Makowsky. Characterizing specification language which admit initial semantics. Theoretical Computer Science, 31(1+2):59–60, 1984.
A. I. Mal’cev. Quasiprimitive classes of abstract algebras. In The Metamathematics of Algebraic Systems, Collected Papers: 1936–1967. North-Holland, 1971. Originally published in Dokl. Akad. Nauk SSSR 108, 187–189, 1956.
Lawrence Moss. Coalgebraic logic. Annals of Pure and Applied Logic, 96:277–317, 1999.
Dirk Pattinson. Semantical principles in the modal logic of coalgebras. In Proceedings 18th International Symposium on Theoretical Aspects of Computer Science (STACS 2001), volume 2010 of LNCS, Berlin, 2001. Springer. Also available as technical report at http://www.informatik.uni-muenchen.de/~pattinso/.
Horst Reichel. An approach to object semantics based on terminal co-algebras. Mathematical Structures in Computer Science, 5(2):129–152, June 1995.
Horst Reichel, editor. Coalgebraic Methods in Computer Science (CMCS’00), volume 33 of Electronic Notes in Theoretical Computer Science, 2000.
Grigore Roşu. Equational axiomatizability for coalgebra. Theoretical Computer Science, 260:229–247, 2001.
Martin Röβiger. Coalgebras and modal logic. In Horst Reichel, editor, Coalgebraic Methods in Computer Science (CMCS’00), volume 33 of Electronic Notes in Theoretical Computer Science, pages 299–320, 2000.
J. Rothe, H. Tews, and B. Jacobs. The coalgebraic class specification language CCSL. Journal of Universal Computer Science, 7(2):175–193, 2001.
J.J.M.M. Rutten. Universal coalgebra: A theory of systems. Theoretical Computer Science, 249:3–80, 2000. First appeared as technical report CS R 9652, CWI, Amsterdam, 1996.
Tobias Schröder, January 2001. Personal Communication.
Andrzej Tarlecki. On the existence of free models in abstract algebraic institutions. Theoretical Computer Science, 37:269–304, 1986. Preliminary version, University of Edinburgh, Computer Science Department, Report CSR-165-84, 1984.
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Kurz, A. (2002). Logics Admitting Final Semantics. In: Nielsen, M., Engberg, U. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2002. Lecture Notes in Computer Science, vol 2303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45931-6_17
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DOI: https://doi.org/10.1007/3-540-45931-6_17
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