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Characterising Behavioural Equivalence: Three Sides of One Coin

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Algebra and Coalgebra in Computer Science (CALCO 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5728))

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Abstract

We relate three different, but equivalent, ways to characterise behavioural equivalence for set coalgebras. These are: using final coalgebras, using coalgebraic languages that have the Hennessy- Milner property and using coalgebraic languages that have “logical congruences”. On the technical side the main result of our paper is a straightforward construction of the final T-coalgebra of a set functor using a given logical language that has the Hennessy-Milner property with respect to the class of T-coalgebras.

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References

  1. Aczel, P., Mendler, N.P.: A final coalgebra theorem. Category Theory and Computer Science, 357–365 (1989)

    Google Scholar 

  2. Adámek, J.: A logic of coequations. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 70–86. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Adámek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories: The Joy of Cats. John Wiley & Sons, Chichester (1990)

    MATH  Google Scholar 

  4. Blackburn, P., de Rijke, M., Venema, Y.: Modal logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  5. Goguen, J., Malcolm, G.: A hidden agenda. Theoretical Computer Science 245(1), 55–101 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Goldblatt, R.: Final coalgebras and the Hennessy-Milner property. Annals of Pure and Applied Logic 138(1-3), 77–93 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Goranko, V., Otto, M.: Model Theory of Modal Logic. In: Handbook of Modal Logic, pp. 255–325. Elsevier, Amsterdam (2006)

    Google Scholar 

  8. Gumm, H.P.: Elements of the General Theory of Coalgebras, Tech. report, Rand Africaans University, Johannesburg, South Africa (1999) (preliminary version)

    Google Scholar 

  9. Jacobs, B., Rutten, J.: A tutorial on (co)algebras and (co)induction. EATCS Bulletin 62, 62–222 (1997)

    MATH  Google Scholar 

  10. Kurz, A., Pattinson, D.: Coalgebraic Modal Logic of Finite Rank. Mathematical Structures in Computer Science 15(3), 453–473 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. MacLane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics, vol. 5. Springer, New York (1971)

    MATH  Google Scholar 

  12. Moss, L.S.: Coalgebraic Logic. Annals of Pure and Applied Logic 96(1-3), 277–317 (1999); Erratum published Ann. P. Appl. Log 99, 241–259 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pattinson, D.: Coalgebraic Modal Logic: Soundness, Completeness and Decidability of Local Consequence. Theoretical Computer Science 309(1-3), 177–193 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rutten, J.J.M.M.: Automata and coinduction (an exercise in coalgebra). In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 194–218. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theoretical Computer Science 249(1), 3–80 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Schröder, L.: Expressivity of Coalgebraic Modal Logic: The Limits and Beyond. Theoretical Computer Science 390, 230–247 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Stirling, C.: Modal and temporal properties of processes. Springer, Heidelberg (2001)

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Imperial College London, London, United Kingdom

    Clemens Kupke

  2. Universiteit van Amsterdam, Amsterdam, The Netherlands

    Raul Andres Leal

Authors
  1. Clemens Kupke
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  2. Raul Andres Leal
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Alexander Kurz

  2. Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze, 206, 33100, Udine, Italy

    Marina Lenisa

  3. Faculty of Mathematics, Informatics and Mechanics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Andrzej Tarlecki

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Kupke, C., Leal, R.A. (2009). Characterising Behavioural Equivalence: Three Sides of One Coin. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-03741-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03740-5

  • Online ISBN: 978-3-642-03741-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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