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An algebraic approach to revising propositional rule-based knowledge bases

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Abstract

One of the important topics in knowledge base revision is to introduce an efficient implementation algorithm. Algebraic approaches have good characteristics and implementation method; they may be a choice to solve the problem. An algebraic approach is presented to revise propositional rule-based knowledge bases in this paper. A way is firstly introduced to transform a propositional rule-based knowledge base into a Petri net. A knowledge base is represented by a Petri net, and facts are represented by the initial marking. Thus, the consistency check of a knowledge base is equivalent to the reachability problem of Petri nets. The reachability of Petri nets can be decided by whether the state equation has a solution; hence the consistency check can also be implemented by algebraic approach. Furthermore, algorithms are introduced to revise a propositional rule-based knowledge base, as well as extended logic programming. Compared with related works, the algorithms presented in the paper are efficient, and the time complexities of these algorithms are polynomial.

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References

  1. van Ditmarsch H, vander Hoek W, Kooi B. Public announcement and belief revision. In: Schmidt R A, Pratt-Hartmann I, Reynolds M, et al., eds. Advances in Modal Logic. London: King’s College Publications, 2004. 62–73

    Google Scholar 

  2. Roorda J W, vander Hoek W, Meyer J J. Iterated belief change in multi-agent systems logic. J IGPL, 2003, 11(2): 223–246

    Article  MATH  MathSciNet  Google Scholar 

  3. Reter T, Fink M, Sabbatini G, et al. On properties of update sequences based on causal rejection. Theory Pract Logic Program, 2002, 2: 711–767

    Article  Google Scholar 

  4. Gelfond M, Lifschitz V. Classical negation in logic programs and disjunctive databases. New Generation Comput, 1991, 9: 365–386

    Google Scholar 

  5. Nemela I, Simons P. Efficient implementation of the well-founded and stable model semantics. In: Maher M J, ed. Proc of the International Joint Conference and Symposium on Logic Programming. Cambridge MA: The MIT Press, 1996. 289–303

    Google Scholar 

  6. Alchourron C E, Gardenfors P, Markinson D. On the logic of theory change: partial meet contraction and revision functions. J Symb Logic, 1985, 50(2): 510–530

    Article  MATH  Google Scholar 

  7. Fagin R, Ullman J D, Vardi M Y. On the semantics of updates in databases. In: De Witt D J, Gardarin G, eds. Proc of the Second ACM SIGACT-SIGMOD Symposium on Principle of Database Systems. New York: ACM Press, 1983. 352–365

    Google Scholar 

  8. Ginsberg M L, Smith D E. Reasoning about action I: A possible worlds approach. Art Intel, 1988, 35: 165–195

    Article  MATH  MathSciNet  Google Scholar 

  9. Nebel B. A knowledge level analysis of belief revision. In: Brachman R J, Levesque H J, Reiter R, eds. Proc of the first International Conference on Principles of Knowledge Representation and Reasoning, San Francisco: Morgan Kaufman Publishers, 1989. 301–311

    Google Scholar 

  10. Weber A. Updating propositional formulas. In: Kerschberg L, ed. Proc First Conference on Expert Database Systems, Menlo Park: Benjamin Cummings, 1986. 487–500

    Google Scholar 

  11. Forbus K D. Introducing actions into qualitative simulation. In: Sridharan N S, ed. Proc of the International Joint Conference on Artificial Intelligence. San Francisco: Morgan Kaufmann Publishers, 1989. 1273–1278

    Google Scholar 

  12. Delgrande J, Schaub T. A consistency-based approach for belief change. Art Intel, 2003, 151(1&2): 1–41

    Article  MATH  MathSciNet  Google Scholar 

  13. Delgrande J, Schaub T, et al. On computing solutions to belief change scenarios. J Logic Comput, 2004, 14: 801–826

    Article  MATH  MathSciNet  Google Scholar 

  14. Li W. A development calculus for specifications. Sci China Ser F-Inf Sci, 2003, 46(5): 390–400

    Article  MATH  Google Scholar 

  15. Luan S, Dai G, Li W. A programmable approach to maintenance of a finite knowledge base. J Comput Sci Tech, 2003, 18(1): 102–108

    Article  MATH  MathSciNet  Google Scholar 

  16. Darwiche A, Pearl J. On the logic of iterated belief revision. Art Intel, 1997, 89(1&2): 1–29

    Article  MATH  MathSciNet  Google Scholar 

  17. Boutilier C. Revision sequences and nested conditionals. In: Bajcsy R, ed. Proc of the 13th International Joint Conference on Artificial Intelligence. San Francisco: Morgan Kaufmann Publishers, 1993. 519–525

    Google Scholar 

  18. Luan S, Dai G, Li W. A programmable approach to revising knowledge bases. Sci China Ser F-Inf Sci, 2005, 48(6): 681–692

    Article  MATH  MathSciNet  Google Scholar 

  19. Dixon S E, Wocke W R. The implementation f a first-order logic AGM belief revision system. In: Bajcsy R, ed. Proc of the 13th International Joint Conference on Artificial Intelligence. San Francisco: Morgan Kaufmann Publishers, 1993. 534–539

    Google Scholar 

  20. Luan S, Dai G. Fast algorithms for revision of some special propositional knowledge bases. J Comput Sci Tech, 2003, 18(3): 388–392

    MATH  MathSciNet  Google Scholar 

  21. Rodrigues O, Benevides M. Belief revision in pseudo-definite sets. In: Pequeno T, Carvalho F, eds. Proc of the 11th Brazilian Symposium on Artificial Intelligence. Berlin: Springer-Verlag, 1994. 157–171

    Google Scholar 

  22. Damàsio C V, Nejdl W, Pereira L P. REVISE: An extended logic programming systems for revising knowledge bases. In: Doyle J, Sandewall E, Torasso P, eds. Proc of the International Conference on Knowledge Representation and Reasoning. San Francisco: Morgan Kaufmann Publishers, 1994. 607–618

    Google Scholar 

  23. Khomenko V, Koutny M, Vogler W. Canonical prefixes of Petri net unfoldings. Acta Inf, 2003, 40(2): 95–118

    Article  MATH  MathSciNet  Google Scholar 

  24. Zhang D, Nguyen D. PREPARE: A tool for knowledge base verification. IEEE Trans Knowledge and Data Engineering, 1994, 6(6): 983–989

    Article  Google Scholar 

  25. Steinmetz R, Theissen S. Integration of Petri nets into a tool for consistency checking of expert systems with rule based knowledge representation. In: Rozenberg G, ed. The 6th European Workshop on Applications and Theory of Petri Nets, Berlin: Springer-Verlag, 1985. 35–52

    Google Scholar 

  26. Meseguer P. A new method to checking rule bases for inconsistency: a Petri net approach. In: Aiello L, ed. Proc of the 9th European Conference on Artificial Intelligence. London: Pitman Publishing, 1990. 437–442

    Google Scholar 

  27. Murata T. Petri nets: properties, analysis and applications. Proc of the IEEE, 1989, 77(4): 541–580

    Article  Google Scholar 

  28. Wu Z. An Introduction to Petri Net (in Chinese). Beijing: China Machine Press, 2006

    Google Scholar 

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Authors and Affiliations

  1. School of Computer Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Luan ShangMin

  2. Institute of Software, Chinese Academy of Sciences, Beijing, 100080, China

    Luan ShangMin & Dai GuoZhong

Authors
  1. Luan ShangMin
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  2. Dai GuoZhong
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Correspondence to Luan ShangMin.

Additional information

Supported by the National Grand Fundamental Research 973 Program of China (Grant No. 2002CB312103)

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Luan, S., Dai, G. An algebraic approach to revising propositional rule-based knowledge bases. Sci. China Ser. F-Inf. Sci. 51, 240–257 (2008). https://doi.org/10.1007/s11432-008-0021-5

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  • DOI: https://doi.org/10.1007/s11432-008-0021-5

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