Terminal Coalgebras for Measure-Polynomial Functors

  • Christoph Schubert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


We use the Kolmogorov Consistency Theorem from Measure Theory to construct terminal coalgebras for a large class of functors on the category of measurable spaces. In particular, we construct terminal stochastic relations and terminal labelled Markov processes. We use this constructions to provide extended expressivity results for canonical interpretations of modal and temporal logics in these structures.


Modal Logic Measurable Space Terminal Sequence Forgetful Functor Countable Product 
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  1. 1.
    Adamék, J.: Introduction to coalgebra. Theory and Applications of Categories 14(8), 157–199 (2005)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Adamek, J., Herrlich, H., Strecker, G.: Abstract and Concrete Categories. Wiley Interscience, Hoboken (1991), Google Scholar
  3. 3.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous time Markov chains. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003)CrossRefGoogle Scholar
  4. 4.
    Doberkat, E.-E.: Stochastic Relations. Foundations for Markov Transition Systems. Chapman & Hall/CRC Press, Boca Raton (2007)zbMATHGoogle Scholar
  5. 5.
    Doberkat, E.-E., Schubert, C.: Coalgebraic logic for stochastic right coalgebras. Ann. Pure Appl. Logic (2009), doi:10.1016/j.apal.2008/06/018Google Scholar
  6. 6.
    Doob, J.L.: Measure theory. Graduate Texts in Mathematics, vol. 143. Springer, New York (1994)zbMATHGoogle Scholar
  7. 7.
    Kechris, A.S.: Classical Descriptive Set Theory. Graduate Texts in Mathematics. Springer, Heidelberg (1994)Google Scholar
  8. 8.
    Moss, L., Viglizzo, I.: Final coalgebras for functors on measurable spaces. Information and Computation 204, 610–636 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Schubert, C.: Coalgebraic logic over analytic spaces. Technical Report 170, Chair for Software Technology, Technische Universität Dortmund (January 2008)Google Scholar
  10. 10.
    Schubert, C.: Final coalgebras for measure-polynomial functors. Technical Report 175, Chair for Software Technology, Technische Universität Dortmund (December 2008)Google Scholar
  11. 11.
    van Breugel, F., Mislove, M., Ouaknine, J., Worrell, J.: Domain theory, testing and simulation for labelled Markov processes. Theoretical Computer Science 333, 171–197 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Viglizzo, I.D.: Coalgebras on measurable spaces. PhD thesis, Indiana University (2005)Google Scholar
  13. 13.
    Viglizzo, I.D.: Final sequences and final coalgebras for measurable spaces. In: Fiadeiro, J.L., Harman, N.A., Roggenbach, M., Rutten, J. (eds.) CALCO 2005. LNCS, vol. 3629, pp. 395–407. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Worrell, J.: Terminal coalgebras for accessible endofunctors. Electronic Notes in Theoretical Computer Science 19, 39–54 (1999)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christoph Schubert
    • 1
  1. 1.Chair for Software TechnologyTechnische Universität Dortmund 

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