A Logic Based Approach to the Static Analysis of Production Systems

  • Jos de Bruijn
  • Martín Rezk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5837)

Abstract

In this paper we present an embedding of propositional production systems into μ-calculus, and first-order production systems into fixed-point logic, with the aim of using these logics for the static analysis of production systems with varying working memories. We encode properties such as termination and confluence in these logics, and briefly discuss which ones cannot be expressed, depending on the expressivity of the logic. We show how the embeddings can be used for reasoning over the production system, and use known results to obtain upper bounds for special cases. The strong correspondence between the structure of the models of the encodings and the runs of the production systems enables the straightforward modeling of properties of the system in the logic.

Keywords

Production System Computation Tree Linear Temporal Logic Kripke Model Resolution Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Kozen, D.: Results on the propositional μ-calculus. In: Proceedings of the 9th Colloquium on Automata, Languages and Programming, London, UK, pp. 348–359. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  2. 2.
    Gurevich, Y., Shelah, S.: Fixed-point extensions of first-order logic. In: Symposium on Foundations of Computer Science, pp. 346–353 (1985)Google Scholar
  3. 3.
    Forgy, C.: Rete: A fast algorithm for the many patterns/many objects match problem. Artif. Intell. 19(1), 17–37 (1982)CrossRefGoogle Scholar
  4. 4.
    Grädel, E.: Guarded fixed point logics and the monadic theory of countable trees. Theor. Comput. Sci. 288(1), 129–152 (2002)MATHCrossRefGoogle Scholar
  5. 5.
    McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 4, pp. 463–502. Edinburgh University press, Edinburgh (1969)Google Scholar
  6. 6.
    Baral, C., Lobo, J.: Characterizing production systems using logic programming and situation calculus, http://www.public.asu.edu/~cbaral/papers/char-prod-systems.ps
  7. 7.
    Kautz, H., Selman, B.: Planning as satisfiability. In: ECAI 1992: Proceedings of the 10th European Conference on Artificial Intelligence, New York, NY, USA, pp. 359–363. John Wiley & Sons, Inc., Chichester (1992)Google Scholar
  8. 8.
    Reiter, R.: Knowledge in Action. Logical Foundations for Specifying and Implementing Dynamical Systems. MIT Press, Cambridge (2001)MATHGoogle Scholar
  9. 9.
    Mattmller, R., Rintanen, J.: Planning for temporally extended goals as propositional satisfiability. In: Veloso, M. (ed.) Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, January 2007, pp. 1966–1971. AAAI Press, Menlo Park (2007)Google Scholar
  10. 10.
    Cerrito, S., Mayer, M.C.: Using linear temporal logic to model and solve planning problems. In: Giunchiglia, F. (ed.) AIMSA 1998. LNCS (LNAI), vol. 1480, p. 141. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    De Giacomo, G., Lenzerini, M.: Pdl-based framework for reasoning about actions. In: AI*IA 1995: Proceedings of the 4th Congress of the Italian Association for Artificial Intelligence on Topics in Artificial Intelligence, London, UK, pp. 103–114. Springer, Heidelberg (1995)Google Scholar
  12. 12.
    Aiken, A., Hellerstein, J.M., Widom, J.: Static analysis techniques for predicting the behavior of active database rules. ACM Transactions on Database Systems 20, 3–41 (1995)CrossRefGoogle Scholar
  13. 13.
    Baralis, E., Ceri, S., Paraboschi, S.: Compile-time and runtime analysis of active behaviors. IEEE Trans. on Knowl. and Data Eng. 10(3), 353–370 (1998)CrossRefGoogle Scholar
  14. 14.
    Baralis, E., Torino, P.D., Widom, J., Widom, N.J.: An algebraic approach to static analysis of active database rules. ACM TODS 25, 269–332 (2000)CrossRefGoogle Scholar
  15. 15.
    Bailey, J., Dong, G., Ramamohanarao, K.: Decidability and undecidability results for the termination problem of active database rules. In: Proceedings of the 17th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 264–273 (1998)Google Scholar
  16. 16.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)MATHGoogle Scholar
  17. 17.
    Courcelle, B.: The expression of graph properties and graph transformations in monadic second-order logic, pp. 313–400. World Scientific, Singapore (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jos de Bruijn
    • 1
  • Martín Rezk
    • 1
  1. 1.KRDB Research CenterFree University of Bozen-BolzanoItaly

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