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Infinitary domain logic for finitary transition systems

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Theoretical Aspects of Computer Software (TACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1281))

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Abstract

The Lindenbaum algebra generated by the Abramsky finitary logic is a distributive lattice dual to an SFP-domain obtained as a solution of a recursive domain equation. We extend Abramsky's result by proving that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual to the same SFP-domain. As a consequence soundness and completeness of the infinitary logic is obtained for the class of finitary transition systems. A corollary of this result is that the same holds for the infinitary Hennessy-Milner logic.

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References

  1. Abramsky, S.: Domain theory and the logic of observable properties. PhD thesis, Queen Mary College, University of London, 1987.

    Google Scholar 

  2. Abramsky, S.: Domain theory in logical form. Annals of Pure and Applied Logic, 51(1):1–77, 1991.

    Google Scholar 

  3. Abramsky, S.: A domain equation for bisimulation. Information and Computation, 92(2):161–218, 1991.

    Google Scholar 

  4. Abramsky, S., Vickers, S.J.: Quantales, observational logic and process semantics. Mathematical Structures in Computer Science, 3:161–227, 1993.

    Google Scholar 

  5. Bonsangue, M.M., Kwiatkowska M.Z.: Re-interpreting the modal μ-calculus. In A. Ponse, M. de Rijke, and Y. Venema, editors, Modal Logic and Process Algebra, volume 53 of CSLI Lecture notes, pages 65–83, Stanford, 1995. Centre for Study of Languages and Information.

    Google Scholar 

  6. Bonsangue, M.M., Jacobs, B., Kok, J.N.: Duality beyond sober spaces: topological spaces and observation frames. Theoretical Computer Science, 151(1):79–124, 1995.

    Google Scholar 

  7. Bonsangue, M.M.: Topological Dualities in Semantics. PhD thesis, Vrije Universiteit Amsterdam, 1996.

    Google Scholar 

  8. Brookes, S.D.: An axiomatic treatment of a parallel programming language. In R. Parikh, editor, Logics of Programs, volume 193 of Lecture Notes in Computer Science, Springer-Verlag, 1985.

    Google Scholar 

  9. Errington, L., Hankin, C.L., Jensen, T.P.: Reasoning about Gamma programs. In G.L. Burn, S.J. Gay, M.D. Ryan, editors, Theory and Formal Methods 1993, Workshop in Computing, Imperial College, London, Springer-Verlag, 1993.

    Google Scholar 

  10. Esakia, L.: Topological Kripke models. Soviet Mathematics Doklady, 15:147–151, 1974.

    Google Scholar 

  11. Fine, K.: Some connections between elementary and modal logic. In S. Kange, editor, Proceedings of the Third Scandinavian Logic Symposium, 1–15, North-Holland, Amsterdam, 1973.

    Google Scholar 

  12. Gay, S.J., Hankin, C.L.: A program logic for Gamma. In J.-M. Andreoli, C.L. Hankin and D. Le Meétayer, editors, Coordination Programming, mechanisms, models and semantics, 167–178, Imperial College Press, London, 1996.

    Google Scholar 

  13. Guessarian, I.: Algebraic Semantics. Volume 99 of Lecture Notes in Computer Science, Springer-Verlag, 1981.

    Google Scholar 

  14. Hennessy, M.C, Milner R.: Algebraic laws for non-determinism and concurrency. Journal of the ACM, 32(1):137–161, 1985.

    Google Scholar 

  15. Johnstone, P.T.: Stone Spaces. Volume 3 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, volume 3, 1982.

    Google Scholar 

  16. Milner, R.: A Calculus of Communicating Systems. Volume 92 of Lecture Notes in Computer Science, Springer-Verlag, 1980.

    Google Scholar 

  17. Park, D.M.: Concurrency and automata on infinite sequences. In P. Deussen, editor, Proceedings of the 5th GI Conference, volume 104 of Lecture Notes in Computer Science, pages 167–183. Springer-Verlag, 1981.

    Google Scholar 

  18. G.D. Plotkin, G.D.: Post-graduate lecture notes in advanced domain theory (incorporating the ‘Pisa notes'). Department of Computer Science, University of Edinburgh, 1981.

    Google Scholar 

  19. Plotkin, G.D.: A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, 1981.

    Google Scholar 

  20. Scott, D.S.: Outline of a mathematical theory of computation. In Proceedings 4th Annual Princeton Conference on Information Sciences and Systems, pages 169–176, 1970.

    Google Scholar 

  21. Scott, D.S.: Domains for denotational semantics. In M. Nielsen and E.M. Schmidt, editors, 9th International Colloquium on Automata, Languages and Programming, Aarhus, Denmark, volume 140 of Lecture Notes in Computer Science, pages 577–613. Springer-Verlag, 1982.

    Google Scholar 

  22. Smyth, M.B.: Power domains and predicate transformers: a topological view. In J. Diaz, editor, Proceedings 10th International Colloquium on Automata, Languages and Programming, Barcelona, Spain, volume 154 of Lecture Notes in Computer Science, pages 662–675. Springer-Verlag, 1983.

    Google Scholar 

  23. Scott, D.S., Strachey, C.: Towards a mathematical semantics for computer languages. In Proceedings of the Symposium on Computers and Automata, volume 21 of Microwave Research Institute Symposia series, 1971.

    Google Scholar 

  24. Vickers, S.J.: Topology via Logic. Volume 5 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 1989.

    Google Scholar 

  25. Zhang, G.-Q.: Logic of Domains. Progress in Theoretical Computer Science, Birkhauser,1991.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Rijks Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, Netherlands

    Marcello M. Bonsangue & Joost N. Kok

Authors
  1. Marcello M. Bonsangue
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  2. Joost N. Kok
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Editor information

Martín Abadi Takayasu Ito

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© 1997 Springer-Verlag Berlin Heidelberg

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Bonsangue, M.M., Kok, J.N. (1997). Infinitary domain logic for finitary transition systems. In: Abadi, M., Ito, T. (eds) Theoretical Aspects of Computer Software. TACS 1997. Lecture Notes in Computer Science, vol 1281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014553

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  • DOI: https://doi.org/10.1007/BFb0014553

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63388-4

  • Online ISBN: 978-3-540-69530-1

  • eBook Packages: Springer Book Archive

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