Model-Checking Over Multi-Valued Logics

  • Marsha Chechik
  • Steve Easterbrook
  • Victor Petrovykh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2021)


Classical logic cannot be used to effectively reason about systems with uncertainty (lack of essential information) or inconsistency (contradictory information often occurring when information is gathered from multiple sources). In his paper we propose the use of quasi-boolean multi-valued logics for reasoning about such systems.We also give semantics to a multi-valued extension of CTL, describe an implementation of a symbolic multi-valued CTL model-checker called χchek, and analyze its correctness and running time.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.R. Anderson and N.D. Belnap. Entailment. Vol. 1. Princeton University Press, 1975.Google Scholar
  2. 2.
    R.-J. Back and J. von Wright. Refinement Calculus: A Systematic Approach. Springer-Verlag, 1998.Google Scholar
  3. 3.
    N.D. Belnap. “A Useful Four-Valued Logic”. In Dunn and Epstein, editors, Modern Uses of Multiple-Valued Logic, pages 30–56. Reidel, 1977.Google Scholar
  4. 4.
    L. Bolc and P. Borowik. Many-Valued Logics. Springer-Verlag, 1992.Google Scholar
  5. 5.
    R. E. Bryant. “Symbolic Boolean manipulation with ordered binary-decision diagrams”. Computing Surveys, 24(3):293–318, September 1992.CrossRefGoogle Scholar
  6. 6.
    T. Bultan, R. Gerber, and C. League. “Composite Model Checking: Verification with Type-Specific Symbolic Representations”. ACM Transactions on Software Engineering and Methodology, 9(1):3–50, January 2000.Google Scholar
  7. 7.
    T. Bultan, R. Gerber, and W. Pugh. “Symbolic Model Checking of Infinite State Programs Using Presburger Arithmetic”. In Proceedings of International Conference on Computer-Aided Verification, Haifa, Israel, 1997.Google Scholar
  8. 8.
    M. Chechik. “On Interpreting Results of Model-Checking withAbstraction”. CSRGTechnical Report 417, University of Toronto, Department of Computer Science, September 2000.Google Scholar
  9. 9.
    M. Chechik, B. Devereux, and S. Easterbrook. “Implementing a Multi-Valued Symbolic Model-Checker”. In Proceedings of TACAS’01, April 2001.Google Scholar
  10. 10.
    E.M. Clarke, E.A. Emerson, and A.P. Sistla. “Automatic Verification of Finite-State Concurrent Systems Using Temporal Logic Specifications”. ACM Transactions on Programming Languages and Systems, 8(2):244–263, April 1986.zbMATHGoogle Scholar
  11. 11.
    E.W. Dijkstra and C.S. Scholten. Predicate Calculus and Program Semantics. Springer, 1990.Google Scholar
  12. 12.
    D.L. Dill. “The Mur-Verification System”. In R. Alur and T.A. Henzinger, editors, Computer-Aided Verification Computer, volume 1102 of Lecture Notes in Computer Science, pages 390–393, NewYork, N.Y., 1996. Springer-Verlag.Google Scholar
  13. 13.
    J.M. Dunn. “A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation”. In Dov Gabbay and Heinrich Wansing, editors, What is Negation. Kluwer Academic Publishers, 1999.Google Scholar
  14. 14.
    S. Easterbrook and M. Chechik. “A Framework for Multi-Valued Reasoning over Inconsistent Viewpoints”. In Proceedings of International Conference on Software Engineering (ICSE’01), May 2001.Google Scholar
  15. 15.
    C. Ghezzi and B. A. Nuseibeh. “Introduction to the Special Issue on Managing Inconsistency in Software Development”. IEEE Transactions on Software Engineering, 24(11):906–1001, November 1998.Google Scholar
  16. 16.
    S. Hazelhurst. Compositional Model Checking of Partially Ordered State Spaces. PhD thesis, Department of Computer Science, University of British Columbia, 1996.Google Scholar
  17. 17.
    S. Hazelhurst. “Generating and Model Checking a Hierarchy of Abstract Models”. Technical Report TR-Wits-CS-1999-0, Department of Computer Science University of the Witwatersrand, Johannesburg, South Africa, March 1999.Google Scholar
  18. 18.
    E.C.R. Hehner. A Practical Theory of Programming. Texts and Monographs in Computer Science. Springer-Verlag, NewYork, 1993.Google Scholar
  19. 19.
    G.J. Holzmann. “The Model Checker SPIN”. IEEE Transactions on Software Engineering, 23(5):279–295, May 1997.MathSciNetGoogle Scholar
  20. 20.
    A. Hunter. “Paraconsistent Logics”. In D. Gabbay and Ph. Smets, editors, Handbook of Defeasible Reasoning and Uncertain Information, volume 2. Kluwer, 1998.Google Scholar
  21. 21.
    A. Hunter and B. Nuseibeh. “Managing Inconsistent Specifications: Reasoning, Analysis and Action”. ACM Transactions on Software Engineering and Methodology, 7(4):335–367, October 1998.Google Scholar
  22. 22.
    M. Huth and M. Ryan. Logic in Computer Science: Modeling and Reasoning About Systems. Cambridge University Press, 2000.Google Scholar
  23. 23.
    S. C. Kleene. Introduction to Metamathematics. NewYork: Van Nostrand, 1952.Google Scholar
  24. 24.
    K.L. McMillan. Symbolic Model Checking. Kluwer Academic, 1993.Google Scholar
  25. 25.
    T.J. Menzies, S. Easterbrook, B. Nuseibeh, and S. Waugh. “An Empirical Investigation of Multiple Viewpoint Reasoning in Requirements Engineering”. In Proceedings of the Fourth International Symposium on Requirements Engineering (RE’99), Limerick, Ireland, June 7-11 1999. IEEE Computer Society Press.Google Scholar
  26. 26.
    G. Priest and K. Tanaka. “Paraconsistent Logic”. In The Stanford Encyclopedia of Philosophy. Stanford University, 1996.Google Scholar
  27. 27.
    H. Rasiowa. An Algebraic Approach to Non-Classical Logics. Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland, 1978.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marsha Chechik
    • 1
  • Steve Easterbrook
    • 1
  • Victor Petrovykh
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada

Personalised recommendations