Skip to main content
SpringerLink
Log in

Measuring Disagreement Among Knowledge Bases

  • Conference paper
  • First Online:
Scalable Uncertainty Management (SUM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11142))

Included in the following conference series:

  • 416 Accesses

Abstract

When combining beliefs from different sources, often not only new knowledge but also conflicts arise. In this paper, we investigate how we can measure the disagreement among sources. We start our investigation with disagreement measures that can be induced from inconsistency measures in an automated way. After discussing some problems with this approach, we propose a new measure that is inspired by the \(\eta \)-inconsistency measure. Roughly speaking, it measures how well we can satisfy all sources simultaneously. We show that the new measure satisfies desirable properties, scales well with respect to the number of sources and illustrate its applicability in inconsistency-tolerant reasoning.

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

References

  1. Kalyanpur, A., Parsia, B., Sirin, E., Cuenca-Grau, B.: Repairing unsatisfiable concepts in OWL ontologies. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 170–184. Springer, Heidelberg (2006). https://doi.org/10.1007/11762256_15

    Chapter  Google Scholar 

  2. Lehmann, J., Bühmann, L.: ORE - a tool for repairing and enriching knowledge bases. In: Patel-Schneider, P.F., et al. (eds.) ISWC 2010. LNCS, vol. 6497, pp. 177–193. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17749-1_12

    Chapter  Google Scholar 

  3. Benferhat, S., Dubois, D., Prade, H.: Some syntactic approaches to the handling of inconsistent knowledge bases: a comparative study part 1: the flat case. Studia Logica 58(1), 17–45 (1997)

    Article  MathSciNet  Google Scholar 

  4. Arieli, O., Avron, A., Zamansky, A.: What is an ideal logic for reasoning with inconsistency? In: IJCAI 2011, pp. 706–711 (2011)

    Google Scholar 

  5. Priest, G.: Paraconsistent logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, pp. 287–393. Springer, Dordrecht (2002). https://doi.org/10.1007/978-94-017-0460-1_4

    Chapter  Google Scholar 

  6. Knight, K.: Measuring inconsistency. J. Philos. Log. 31(1), 77–98 (2002)

    Article  MathSciNet  Google Scholar 

  7. Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. J. Intell. Inf. Syst. 27(2), 159–184 (2006)

    Article  Google Scholar 

  8. Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 191–236. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30597-2_7

    Chapter  Google Scholar 

  9. Thimm, M.: Measuring inconsistency in probabilistic knowledge bases. In: UAI 2009, pp. 530–537. AUAI Press (2009)

    Google Scholar 

  10. Muiño, D.P.: Measuring and repairing inconsistency in probabilistic knowledge bases. Int. J. Approx. Reason. 52(6), 828–840 (2011)

    Article  MathSciNet  Google Scholar 

  11. Potyka, N.: Linear programs for measuring inconsistency in probabilistic logics. In: KR 2014, pp. 568–577 (2014)

    Google Scholar 

  12. Potyka, N., Thimm, M.: Probabilistic reasoning with inconsistent beliefs using inconsistency measures. In: IJCAI 2015, pp. 3156–3163 (2015)

    Google Scholar 

  13. Konieczny, S.: On the difference between merging knowledge bases and combining them. In: KR, pp. 135–144 (2000)

    Google Scholar 

  14. Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: KR 2008, pp. 358–366 (2008)

    Google Scholar 

  15. Thimm, M.: On the compliance of rationality postulates for inconsistency measures: a more or less complete picture. KI-Künstliche Intelligenz 31, 1–9 (2016)

    Google Scholar 

  16. Besnard, P.: Revisiting postulates for inconsistency measures. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 383–396. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11558-0_27

    Chapter  Google Scholar 

  17. Zwicker, W.: Introduction to the theory of voting. In: Handbook of Computational Social Choice, pp. 23–56 (2016)

    Google Scholar 

  18. Hunter, A., Konieczny, S.: On the measure of conflicts: shapley inconsistency values. Artif. Intell. 174(14), 1007–1026 (2010)

    Article  MathSciNet  Google Scholar 

  19. Matousek, J., Gärtner, B.: Understanding and Using Linear Programming. Universitext. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-30717-4

    Book  MATH  Google Scholar 

  20. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-29953-X

    Book  MATH  Google Scholar 

  21. Hansen, P., Jaumard, B.: Probabilistic satisfiability. In: Kohlas, J., Moral, S. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, pp. 321–367. Springer, Dordrecht (2000). https://doi.org/10.1007/978-94-017-1737-3_8

    Chapter  Google Scholar 

  22. Whitworth, B., Felton, R.: Measuring disagreement in groups facing limited-choice problems. ACM SIGMIS Database 30(3–4), 22–33 (1999)

    Article  Google Scholar 

  23. Liu, W.: Analyzing the degree of conflict among belief functions. Artif. Intell. 170(11), 909–924 (2006)

    Article  MathSciNet  Google Scholar 

  24. Castiñeira, E.E., Cubillo, S., Montilla, W.: Measuring incompatibility between atanassovs intuitionistic fuzzy sets. Inf. Sci. 180(6), 820–833 (2010)

    Article  MathSciNet  Google Scholar 

  25. Jousselme, A.L., Maupin, P.: Distances in evidence theory: comprehensive survey and generalizations. Int. J. Approx. Reason. 53(2), 118–145 (2012)

    Article  MathSciNet  Google Scholar 

  26. Thimm, M.: Coherence and compatibility of markov logic networks. In: ECAI 2014, pp. 891–896. IOS Press (2014)

    Google Scholar 

  27. Grant, J., Hunter, A.: Distance-based measures of inconsistency. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS (LNAI), vol. 7958, pp. 230–241. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39091-3_20

    Chapter  Google Scholar 

  28. Baral, C., Kraus, S., Minker, J.: Combining multiple knowledge bases. IEEE Trans. Knowl. Data Eng. 3(2), 208–220 (1991)

    Article  Google Scholar 

  29. Liberatore, P., Schaerf, M.: Arbitration (or how to merge knowledge bases). IEEE Trans. Knowl. Data Eng. 10(1), 76–90 (1998)

    Article  Google Scholar 

  30. Konieczny, S., Pérez, R.P.: Logic based merging. J. Philos. Log. 40(2), 239–270 (2011)

    Article  MathSciNet  Google Scholar 

  31. Grégoire, É., Konieczny, S., Lagniez, J.: On consensus extraction. In: IJCAI 2016, pp. 1095–1101. AAAI Press, New York (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Osnabrück, Osnabrück, Germany

    Nico Potyka

Authors
  1. Nico Potyka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nico Potyka .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  3. Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Potyka, N. (2018). Measuring Disagreement Among Knowledge Bases. In: Ciucci, D., Pasi, G., Vantaggi, B. (eds) Scalable Uncertainty Management. SUM 2018. Lecture Notes in Computer Science(), vol 11142. Springer, Cham. https://doi.org/10.1007/978-3-030-00461-3_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-00461-3_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00460-6

  • Online ISBN: 978-3-030-00461-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation