Domains of View: A Foundation for Specification and Analysis

Conference paper
Part of the Semantic Structures in Computation book series (SECO, volume 1)


We propose a platform for the specification and analysis of systems. This platform contain models, their refinement and abstraction, and a temporal logic semantics; rendering a sound framework for property validation and refutation. The platform is parametric in a domain of view, an abstraction of a construction based on the Plotkin power domain. For each domain of view E, the resulting platform P [E]1 contains partial,incomplete systems and complete systems — the actual implementations. Complete systems correspond to the platform that has as parameter a domain D that is, as a set, isomorphic to the maximal elements of E. If one restricts P [E] to implementations, but retains the temporal logic semantics, refinement, and abstraction relations, one recovers the platform P [D]. This foundation recasts existing work on modal transition systems, presents fuzzy systems, and ponders on the nature of probabilistic platforms. For domains of view E that are determined by a linearly ordered, complete lattice, we present a category of “relations” as a step toward a view-based semantics of predicate logic.


Modal transition systems refinement abstract interpretation partial systems property verification property refutation fuzzy systems linear t-norms Markov chains Plotkin power domain 


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  1. 1.
    S. Abramsky. A domain equation for bisimulation.Information and Computation, 92:161-218, 1991. CrossRefGoogle Scholar
  2. 2.
    S. Abramsky and A. Jung. Domain theory. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, volume 3, pages 1-168. Clarendon Press,1994.Google Scholar
  3. 3.
    C. Baier. Polynomial Time Algorithms for Testing Probabilistic Bisimulation and Simulation. In Proceedings of CAV’96,number 1102 in Lecture Notes in Computer Science,pages 38-49.Springer Verlag, 1996. Google Scholar
  4. 4.
    C. Baier and H. Hermanns.Weak bisimulation for fully probabilistic processes.In Proc. 9th International Conference on Computer Aided Verification (CAV’97),volume 1254 of Lecture Notes in Computer Science, pages 119-130,1997.Google Scholar
  5. 5.
    J. C. Bradfield.Verifying Temporal Properties Of Systems. Birkhaeuser, Boston, Mass., 1991.Google Scholar
  6. 6.
    J. R. Burch, E. M. Clarke, D. L. Dill, K. L. McMillan, and J. Hwang. Symbolic model checking: 1020 states and beyond. Proceedings of the Fifth Annual Symposium on Logic in Computer Science, June 1990.Google Scholar
  7. 7.
    J. R. Burch, E. M. Clarke, D. L. Dill, K. L. McMillan, and J. Hwang. Symbolic model checking: 1020 states and beyond.Information and Computation, 98(2):142-170, 1992. CrossRefGoogle Scholar
  8. 8.
    E. M. Clarke and E. M. Emerson. Synthesis of synchronization skeletons for branching time temporal logic. In D. Kozen, editor, Proc. Logic of Programs, volume 131 of LNCS. Springer Verlag, 1981. Google Scholar
  9. 9.
    E. M. Clarke, O. Grumberg, and D. E. Long. Model Checking and Abstraction. In 19th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages,pages 343-354. ACM Press, 1992.Google Scholar
  10. 10.
    P. Cousot and R. Cousot. Abstract interpretation: a unified lattice model for static analysis of programs In Proc. 4th ACM Symp. on Principles of Programming Languages,pages 238-252. ACM Press, 1977.Google Scholar
  11. 11.
    R. de Nicola and F. Vaandrager. Three Logics for Branching Bisimulation.Journal of the Association of Computing Machinery,42(2):458-487, March 1995. CrossRefGoogle Scholar
  12. 12.
    M. B. Dwyer and D. A. Schmidt. Limiting State Explosion with Filter-Based Refinement. In Proceedings of the ILPS’97 Workshop on Verification, Model Checking, and Abstraction, 1997.Google Scholar
  13. 13.
    S. Eilenberg and G. M. Kelly. Closed categories. In S. Eilenberg, D. K. Harrison, S. MacLane, and H. Röhrl, editors, Proceedings of the Conference on Categorical Algebra, La Jolla 1965,pages 421-562. Springer Verlag, 1966.Google Scholar
  14. 14.
    J. M. G. Fell. A hausdorff topology for the closed subsets of a locally compact non-hausdorff space. Proc. Amer. Math. Soc., 13:472-476, 1962.CrossRefGoogle Scholar
  15. 15.
    G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott. A Compendium of Continuous Lattices. Springer Verlag, 1980.Google Scholar
  16. 16.
    R. J. van Glabbeek and W. P. Weijland. Branching Time and Abstraction in Bisimulation Semantics. Journal of the ACM, 43(3):555-600, May 1996.Google Scholar
  17. 17.
    C. Gunter. The mixed power domain. Theoretical Computer Science, 103:311-334, 1992.CrossRefGoogle Scholar
  18. 18.
    P. R. Halmos. Measure Theory. D. van Norstrand Company, 1950.Google Scholar
  19. 19.
    R. Heckmann. Power domains and second order predicates. Theoretical Computer Science, 111:59-88, 1993.CrossRefGoogle Scholar
  20. 20.
    M. Huth. A Unifying Framework for Model Checking Labeled Kripke Structures, Modal Transition Systems, and Interval Transition Systems. In 19th International Conference on the Foundations of Software Technology & Theoretical Computer Science, volume 1738 of Lecture Notes in Computer Science, pages 369-380. Springer Verlag, 1999.Google Scholar
  21. 21.
    M. Huth, R. Jagadeesan, and D. Schmidt. Modal transition systems: a foundation for three-valued program analysis. Submitted, October 2000.Google Scholar
  22. 22.
    D. L. Isaacson and R. W. Madsen. Markov Chains Theory and Applications. Probability and Mathematical Statistics. John Wiley & Sons, 1976.Google Scholar
  23. 23.
    B. Jonsson and K. G. Larsen. Specification and Refinement of Probabilistic Processes. In Proceedings of the International Symposium on Logic in Computer Science, pages 266-277. IEEE Computer Society, IEEE Computer Society Press, July 1991.Google Scholar
  24. 24.
    P. Kelb. Model checking and abstraction: a framework preserving both truth and failure information. Technical Report Technical report, OFFIS, University of Oldenburg, Germany, 1994.Google Scholar
  25. 25.
    D. Kozen. Results on the propositional mu-calculus. Theoretical Computer Science, 27:333-354, 1983.CrossRefGoogle Scholar
  26. 26.
    S. Mac Lane. Categories for the Working Mathematician. Springer Verlag, 1971. Google Scholar
  27. 27.
    K. G. Larsen. Modal Specifications. In J. Sifakis, editor, Automatic Verification Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 232-246. Springer Verlag, June 12-14, 1989 1989. International Workshop, Grenoble, France.Google Scholar
  28. 28.
    K. G. Larsen and A. Skou. Bisimulation through Probabilistic Testing.Information and Computation, 94(1):1-28, September 1991.Google Scholar
  29. 29.
    K. G. Larsen and B. Thomsen. A Modal Process Logic. In Third Annual Symposium on Logic in Computer Science, pages 203-210. IEEE Computer Society Press, 1988.Google Scholar
  30. 30.
    R. Milner. A modal characterisation of observable machine behaviours. In G. Astesiano and C. Böhm, editors, CAAP `81, volume 112 of Lecture Notes in Computer Science, pages 25-34. Springer Verlag, 1981.Google Scholar
  31. 31.
    R. Milner. Communication and Concurrency. Prentice-Hall, 1989.Google Scholar
  32. 32.
    R. E. Moore. Interval Analysis. Prentice-Hall, Englewood Cliffs, 1966.Google Scholar
  33. 33.
    D. M. Park. Concurrency on automata and infinite sequences. In P. Deussen, editor, Conference on Theoretical Computer Science,volume 104 of Lecture Notes in Computer Science. Springer Verlag, 1981.Google Scholar
  34. G. D. Plotkin. A powerdomain construction. SIAM Journal on Computing, 5:452-487, 1976.CrossRefGoogle Scholar
  35. 35.
    A. Pnueli. The temporal logic of programs In Proceedings of the 19th Annual Symposium on the Foundations of Computer Science. IEEE Computer Society Press, 1977.Google Scholar
  36. 36.
    A. Pnueli. Applications of temporal logic to the specification and verification of reactive systems: a survey of current trends. In J.W. de Bakker, editor, Current Trends in Concurrency, volume 224 of Lecture Notes in Computer Science, pages 510-584. Springer-Verlag, 1985.Google Scholar
  37. 37.
    D. A. Schmidt. Denotational Semantics. Allyn and Bacon, 1986.Google Scholar
  38. 38.
    D.A. Schmidt. Binary relations for abstraction and refinement. Elsevier Electronic Notes in Computer Science, November 1999. Workshop on Refinement and Abstraction, Amagasaaki, Japan. To appear.Google Scholar
  39. 39.
    B. Schweizer and A. Sklar. Associative functions and abstract semi-groups.Publ. Math. Debrecen,10:69-81, 1963.Google Scholar
  40. 40.
    D. S. Scott. Continuous lattices. In F. Lawvere, editor, Toposes,Algebraic Geometry and Logic, volume 274 of Lecture Notes in Mathematics, pages 97-136. Springer Verlag, 1972.Google Scholar
  41. 41.
    J. M. Spivey. The Z Notation: A Reference Manual. Prentice Hall, 1992. Second edition.Google Scholar
  42. 42.
    J. E. Stoy. Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. The MIT Press, 1977.Google Scholar
  43. 43.
    C. Strachey. Towards a formal semantics. In T. B. Steel, editor, Formal Language Description Languages for Computer Programming, pages 198-220, Amsterdam, 1966. North-Holland.Google Scholar
  44. 44.
    M. Vardi. Automatic Verification of Probabilistic Concurrent Finite-State Programs In Proc. FOCS’85, pages 327-338. IEEE, 1985.Google Scholar
  45. 45.
    L. A. Zadeh. Fuzzy Sets. Information and Control, 8:338-353, 1965.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  1. 1.Department of Computing and Information SciencesKansas State UniversityManhattanUSA

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