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Implementation of Belief Change Operators Using BDDs

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Abstract

While the theory of belief change has attracted a lot of interest from researchers, work on implementing belief change and actually putting it to use in real-world problems is still scarce. In this paper, we present an implementation of propositional belief change using Binary Decision Diagrams. Upper complexity bounds for the algorithm are presented and discussed. The approach is presented both in the general case, as well as on specific belief change operators from the literature. In an effort to gain a better understanding of the empirical efficiency of the algorithms involved, a fault diagnosis problem on combinational circuits is presented, implemented and evaluated.

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References

  1. Andersen, H. R.: 1998, 'An Introduction to Binary Decision Diagrams'. http://www.it.dtu.dk/~hra. Department of Information Technology, Technical University of Denmark, Lecture Notes.

  2. Borgida, A.: 1984, 'Intelligent Handling of Exceptions in Information Systems'. In: Workshop on Expert Database Systems, University of South Carolina, 1984, Vol. 2.

  3. Bryant, R. E.: 1986, 'Graph-Based Algorithms for Boolean Function Manipulation'. IEEE Transactions on Computers C-35(8), 677-691.

    Google Scholar 

  4. Bryant, R. E.: 1992, 'Symbolic Boolean Manipulation with Ordered Binary-Decision Diagrams'. ACM Computing Surveys 24(3), 293-318.

    Google Scholar 

  5. Burch, J. R., J. M. Clarke, K. L. McMillan, D. L. Dill, and J. Hwang: 1990, 'Symbolic model checking: 1020 states and beyond'. In: IEEE Symposium on Logic in Computer Science.

  6. Dalal, M.: 1988, 'Investigations Into a Theory of Knowledge Base Revision: Preliminary Report'. In: Proceedings of the Seventh National Conference on Artificial Intelligence, Vol. 2. St. Paul, Minnesota, pp. 475-479.

    Google Scholar 

  7. Gärdenfors, P.: 1988, Knowledge in Flux: Modeling the Dynamics of Epistemic States. Cambridge, MA: MIT Press, Bradford Books.

    Google Scholar 

  8. Huth, M. R., and M. D. Ryan: 2000, Logic in Computer Science: Modelling and Reasoning about Systems. Cambridge University Press.

  9. Katsuno, H., and A. O. Mendelzon: 1989, 'A Unified View of Propositional Knowledge Base Updates'. In: N. S. Sridharan (ed.): Proceedings of the 11th International Joint Conference on Artificial Intelligence. Detroit, MI, USA, pp. 1413-1419.

  10. Katsuno, H., and A. O. Mendelzon: 1991, 'Propositional Knowledge Base Revision and Minimal Change'. Artificial Intelligence 52(3), 263-294.

    Google Scholar 

  11. Katsuno, H., and A. O. Mendelzon: 1992, 'On the Difference between Updating a Knowledge Base annd Revising it'. In: P. Gärdenfors (ed.): Belief Revision. Cambridge University Press, pp. 183-203.

  12. Lind-Nielsen, J., 'BuDDy: Binary Decision Diagram Package Release 1.8'. http://www.it.dtu.dk/research/buddy.

  13. McMillan, K. L.: 1993, Symbolic Model Checking. Kluwer Academic Publishers.

  14. Reiter, R.: 1987, 'A theory of diagnosis from first principles'. Artificial Intelligence 32, 57-95. Reprinted in in Readings in Nonmonotonic Reasoning, M. L. Ginsberg (ed.), Morgan Kaufman, San Francisco, CA. 1987, pp. 352–371.

    Google Scholar 

  15. Satoh, K.: 1988, 'Nonmonotonic Reasoning by Minimal Belief Revision'. In: I. for New Generation Computer Technology (ICOT) (ed.): Proceedings of the International Conference on Fifth Generation Computer Systems. Volume 2. Berlin, FRG, pp. 455-462.

  16. Somenzi, F., 'CUDD: CU Decision Diagram Package Release 2.3.0'. http://vlsi.colorado.edu/~fabio/CUDD/cuddIntro.html.

  17. Williams, M.-A.: 1997, 'Anytime Belief Revision'. In: Fifteenth International Joint Conference on Artifical Intelligence. pp. 74-81.

  18. Winslett, M.: 1988, 'Reasoning About Action Using a Possible Models Approach'. In: Proceedings of the Seventh National Conference on Artificial Intelligence. pp. 89-93.

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Gorogiannis, N., Ryan, M.D. Implementation of Belief Change Operators Using BDDs. Studia Logica 70, 131–156 (2002). https://doi.org/10.1023/A:1014610426691

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