Skip to main content
SpringerLink
Log in

New tractable classes for default reasoning from conditional knowledge bases

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

This paper refines the tractability/intractability frontier of default reasoning from conditional knowledge bases. It presents two new tractable cases with relation to lexicographic entailment. In particular, we have introduced nested conditional knowledge bases and co-nested conditional knowledge bases, which are meaningful conditional knowledge bases. Both tractable classes presented in this paper can be recognized in linear time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E.W. Adams, The Logic of Conditionals. D. Reidel, Dordrecht, 1 edition, 1975.

  2. S. Benferhat, C. Cayrol, D. Dubois, J. Lang and H. Prade, Inconsistency Management and Prioritized Syntax-Based Entailment, in: IJCAI'93: Proceedings of the Thirteenth International Joint Conferences on Artificial Intelligence (1993) pp. 640–645.

  3. K.S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using P–Q tree algorithms, Journal of Comparative System Science 13 (1976) 335–379.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Cayrol, M.C. Lagasquie-Schiex, and T. Schiex, Nonmonotonic reasoning: From complexity to algorithms. Annals of Mathematics and Artificial Intelligence 22(3–4) (1998) 207–236.

    Article  MATH  MathSciNet  Google Scholar 

  5. V. Chandru and J.N. Hooker, Optimization Methods for Logical Inference, Series in Discrete Mathematics and Optimization (Wiley, 1999).

  6. V. Chandru and V.S. Jayachandran, Maxsat and related problems on extended nested propositions. Research report IISc-CSA-94-12, Computer Science and Automation, Indian Institute of Science, Bangalore, India, 1994.

    Google Scholar 

  7. S.A. Cook, The complexity of theorem-proving procedures, in: ACM Symposium on Theory of Computing (1971) pp. 151–158.

  8. T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein, Introduction to Algorithms (MIT Press, 2001).

  9. T. Eiter and T. Lukasiewicz, Complexity results for default reasoning from conditional knowledge bases, Artificial Intelligence 124(2) (2000) 169–241.

    Article  MATH  MathSciNet  Google Scholar 

  10. M.R. Garey and D.S. Johnson, Computers and Intractability–A Guide to the Theory of NP-Completeness (W. H. Freeman and Company, San Francisco, 1978).

    Google Scholar 

  11. M. Goldszmidt, P. Morris, and J. Pearl, A maximum entropy approach to nonmonotonic reasoning, IEEE Transactions of Pattern Analysis and Machine Intelligence 15(3) (March1993) 220–232.

    Article  Google Scholar 

  12. M. Goldszmidt and J. Pearl, Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artificial Intelligence 84(1–2) (1996) 57–112.

    Article  MathSciNet  Google Scholar 

  13. J. Gu, P.W. Purdom, J. Franco, and B.W. Wah, Algorithms for the satisfiability (SAT) problem: A survey, in: Satisfiability Problem Theory and Applications, eds. D. Du, J. Gu, and P.M. Pardalos, Vol. 35 of DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, (American Mathematical Society, 1997) pp. 19–152.

  14. R.G. Jeroslow, Logic-Based Decision Support. Mixed Integer Model Formulation, Elsevier, Amsterdam, 1988.

    Google Scholar 

  15. R.G. Jeroslow and J. Wang, Solving propositional satisfiability problems. Annals of Mathematics and Artificial Intelligence 1 (1990) 167–187.

    Article  MATH  Google Scholar 

  16. D.S. Johnson, A catalog of complexity classes, in: Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity, Chapter 9, ed. J. van Leeuwen (Elsevier and MIT Press (co-publishers), 1990) pp. 67–161.

  17. D.E. Knuth, Nested satisfiability, Acta Informatica 28(1) (1990) 1–6.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Kratochvíl and M. Křivánek, Satisfiability of co-nested formulas, Acta Informatica 30(4) (1993) 397–403.

    Article  MATH  MathSciNet  Google Scholar 

  19. D. Lehmann, Another perspective on default reasoning, Annals of Mathematics and Artificial Intelligence 15(1) (1995) 61–82.

    Article  MATH  MathSciNet  Google Scholar 

  20. J. Pearl, Probabilistic semantics for nonmonotonic reasoning: A survey, in: KR’89: Principle of Knowledge Representation and Reasoning, eds. R.J. Brachman, H.J. Levesque, and R. Reiter, (Morgan Kufmann, San Mateo, California, 1989) pp. 505–516.

    Google Scholar 

  21. J. Pearl, System Z, A natural ordering of defaults with tractable applications to nonmonotonic reasoning, in: TARK: Theoretical Aspects of Reasoning about Knowledge, ed. R. Parikh (Morgan Kaufmann, 1990) pp. 121–136.

  22. H.P. Williams, Fourier–Motzkin elimination extension to integer programming problems, Journal of Combinatorial Theory (A) 21 (1976) 118–123.

    Article  MATH  Google Scholar 

  23. H.P. Williams, Logic applied to integer programming and integer programming applied to logic, European Journal of Operational Research 81(3) (1995) 605–616.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Universidade Federal do Espírito Santo (UFES), Federal do Espírito Santo, Brazil

    Berilhes Borges Garcia

Authors
  1. Berilhes Borges Garcia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Berilhes Borges Garcia.

Additional information

Responsible editor: Allesandro Cigno

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borges Garcia, B. New tractable classes for default reasoning from conditional knowledge bases. Ann Math Artif Intell 45, 275–291 (2005). https://doi.org/10.1007/s10472-005-9000-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-005-9000-3

Keywords

AMS subject classification

Search

Navigation