Skip to main content
SpringerLink
Log in

Complexity of Model Checking for Cardinality-Based Belief Revision Operators

  • Conference paper
  • First Online:
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10369))

Abstract

This paper deals with the complexity of model checking for belief base revision. We extend the study initiated by Liberatore & Schaerf and introduce two new belief base revision operators stemming from consistent subbases maximal with respect to cardinality. We establish the complexity of the model checking problem for various operators within the framework of propositional logic as well as in the Horn fragment.

This work has received support from the French Agence Nationale de la Recherche, ASPIQ project reference ANR-12-BS02-0003.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The notation RSR comes from the expression “Removed Sets Revision”.

References

  1. Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symbolic Logic 50, 510–530 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benferhat, S., Ben-Naim, J., Papini, O., Würbel, E.: An answer set programming encoding of prioritized removed sets revision: application to GIS. Appl. Intell. 32(1), 60–87 (2010)

    Article  MATH  Google Scholar 

  3. Benferhat, S., Cayrol, C., Dubois, D., Lang, J., Prade, H.: Inconsistency management and prioritized syntax-based entailment. In: Proceedings of IJCAI 1993, pp. 640–645 (1993)

    Google Scholar 

  4. Cayrol, C., Lagasquie-Schiex, M., Schiex, T.: Nonmonotonic reasoning: from complexity to algorithms. Ann. Math. Artif. Intell. 22(3–4), 207–236 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Creignou, N., Pichler, R., Woltran, S.: Do hard sat-related reasoning tasks become easier in the Krom fragment? In: IJCAI (2013)

    Google Scholar 

  6. Creignou, N., Zanuttini, B.: A complete classification of the complexity of propositional abduction. SIAM J. Comput. 36, 207–229 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Eiter, T., Gottlob, G.: On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artif. Intell. 57(2–3), 227–270 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gärdenfors, P.: Belief revision and nonmonotonic logic: Two sides of the same coin? In: Proceedings of ECAI 1990, pp. 768–773 (1990)

    Google Scholar 

  9. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H Freeman, New York (1979)

    MATH  Google Scholar 

  10. Ginsberg, M.: Counterfactuals. Artif. Intell. 30, 35–79 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hansson, S.O.: Revision of belief sets and belief bases. In: Dubois, D., Prade, H. (eds.) Belief Change. Handbook of Defeasible Reasoning and Uncertainty Management Systems, pp. 17–75. Kluwer, Netherlands (1998)

    Chapter  Google Scholar 

  12. Katsuno, H., Mendelzon, A.O.: Propositional knowledge base revision and minimal change. Artif. Intell. 52, 263–294 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lehmann, D.: Belief revision, revised. In: Proceedings of IJCAI 1995, pp. 1534–1540 (1995)

    Google Scholar 

  14. Liberatore, P., Schaerf, M.: Belief revision and update: complexity of model checking. J. Comput. Syst. Sci. 62(1), 43–72 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Nebel, B.: Belief revision and default reasoning: syntax-based approaches. In: Proceedings of KR 1991, pp. 417–428 (1991)

    Google Scholar 

  16. Nebel, B.: How hard is it to revise a belief base? In: Dubois, D., Prade, H. (eds.) Belief Change. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 3, pp. 77–145. Springer, Netherlands (1998)

    Chapter  Google Scholar 

  17. Papadimitriou, C.H.: Computational Complexity. Addison Wesley, Boston (1994)

    MATH  Google Scholar 

  18. Papini, O.: A complete revision function in propositional calculus. In: Proceedings of ECAI 1992, pp. 339–343 (1992)

    Google Scholar 

  19. Stockmeyer, L.J.: The polynomial-time hierarchy. Theor. Comput. Sci. 3(1), 1–22 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wagner, K.: More complicated questions about maxima and minima, and some closures of NP. Theor. Comput. Sci. 51(1–2), 53–80 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  21. Winslett, M.: Sometimes updates are circumscription. In: Proceedings of IJCAI 1989, pp. 859–863 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aix-Marseille Université, CNRS, LIF, LSIS, Marseille, France

    Nadia Creignou & Odile Papini

  2. University of Sfax, ISIMS, Sfax, Tunisia

    Raïda Ktari

Authors
  1. Nadia Creignou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raïda Ktari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Odile Papini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nadia Creignou .

Editor information

Editors and Affiliations

  1. IDSIA, Lugano, Switzerland

    Alessandro Antonucci

  2. ONERA, Toulouse, France

    Laurence Cholvy

  3. Aix-Marseille University, Marseille, France

    Odile Papini

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Creignou, N., Ktari, R., Papini, O. (2017). Complexity of Model Checking for Cardinality-Based Belief Revision Operators. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-61581-3_35

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61580-6

  • Online ISBN: 978-3-319-61581-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation