Skip to main content
SpringerLink
Log in

Measuring Inconsistency in a General Information Space

  • Conference paper
  • First Online:
Foundations of Information and Knowledge Systems (FoIKS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12012))

Abstract

AI systems often need to deal with inconsistent information. For this reason since the early 2000s some AI researchers have developed ways to measure the amount of inconsistency in a knowledge base. By now there is a substantial amount of research about various aspects of inconsistency measuring. The problem is that most of this work applies only to knowledge bases formulated as sets of formulas in propositional logic. Hence this work is not really applicable to the way that information is actually stored. The purpose of this paper is to extend inconsistency measuring to real world information. We first define the concept of general information space which encompasses various types of databases and scenarios in AI systems. Then, we show how to transform any general information space to an inconsistency equivalent propositional knowledge base, and finally apply propositional inconsistency measures to find the inconsistency of the general information space. Our method allows for the direct comparison of the inconsistency of different information spaces, even though the data is presented in different ways. We demonstrate the transformation on three general information spaces: a relational database, a graph database, and a Blocks world scenario, where we apply several inconsistency measures after performing the transformation.

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.

    We assume the reader is familiar with the classical notions of database scheme, relation scheme, relation instance, and integrity constraint. We will recall these notions in Sect. 5.1.

References

  1. Foto, N.A., Kolaitis, P.G.: Repair checking in inconsistent databases: algorithms and complexity. In: Proceedings of International Conference on Database Theory (ICDT), pp. 31–41 (2009)

    Google Scholar 

  2. Bertossi, L.E.: Repair-based degrees of database inconsistency. In: Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), pp. 195–209 (2019)

    Chapter  Google Scholar 

  3. Bertossi, L.E., Hunter, A., Schaub, T.: Introduction to inconsistency tolerance. In: Inconsistency Tolerance, pp. 1–14 (2005)

    Chapter  Google Scholar 

  4. Codd, E.F.: The Relational Model for Database Management, Version 2. Addison-Wesley, Boston (1990)

    MATH  Google Scholar 

  5. De Bona, G., Grant, J., Hunter, A., Konieczny, S.: Towards a unified framework for syntactic inconsistency measures. In: Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI), pp. 1803–1810 (2018)

    Google Scholar 

  6. Doder, D., Raskovic, M., Markovic, Z., Ognjanovic, Z.: Measures of inconsistency and defaults. Int. J. Approximate Reasoning 51(7), 832–845 (2010)

    Article  MathSciNet  Google Scholar 

  7. Eiter, T., Fink, M., Schüller, P., Weinzierl, A.: Finding explanations of inconsistency in multi-context systems. Artif. Intell. 216, 233–274 (2014)

    Article  MathSciNet  Google Scholar 

  8. Fagin, R.: Multivalued dependencies and a new normal form for relational databases. ACM Trans. Database Syst. 2(3), 262–278 (1977)

    Article  Google Scholar 

  9. Gabbay, D.M., Hunter, A.: Making inconsistency respectable: a logical framework for inconsistency in reasoning. In: Proceedings of International Workshop on Fundamentals of Artificial Intelligence Research (FAIR), pp. 19–32 (1991)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  11. Grant, J., Hunter, A.: Measuring consistency gain and information loss in stepwise inconsistency resolution. In: Proceedings of European Conference Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), pp. 362–373 (2011)

    MATH  Google Scholar 

  12. Grant, J., Hunter, A.: Distance-based measures of inconsistency. In: Proceedings of ECSQARU, pp. 230–241 (2013)

    Google Scholar 

  13. Grant, J., Martinez, M.V.: Measuring Inconsistency in Information. College Publications (2018)

    Google Scholar 

  14. Grant, J., Martinez, M.V., Molinaro, C., Parisi, F.: On measuring inconsistency in spatio-temporal databases. In: Grant, J., Martinez, M.V. (eds.) Measuring Inconsistency in Information, volume 73 of Studies in Logic, pp. 313–342. College Publications (2018)

    Google Scholar 

  15. Grant, J., Minker, J.: Inferences for numerical dependencies. Theoret. Comput. Sci. 41, 271–287 (1985)

    Article  MathSciNet  Google Scholar 

  16. Grant, J., Minker, J.: Normalization and axiomatization for numerical dependencies. Inf. Control 65(1), 1–17 (1985)

    Article  MathSciNet  Google Scholar 

  17. Gupta, N., Nau, D.S.: Complexity results for blocks-world planning. In: Proceedings of the 9th National Conference on Artificial Intelligence (AAAI), pp. 629–633 (1991)

    Google Scholar 

  18. Hunter, A.: Measuring inconsistency in knowledge via quasi-classical models. In: Proceedings of National Conference on Artificial Intelligence and Conference on Innovative Applications of Artificial Intelligence (AAAI/IAAI), pp. 68–73 (2002)

    Google Scholar 

  19. Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. In: Inconsistency Tolerance, pp. 191–236 (2005)

    Chapter  Google Scholar 

  20. Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR), pp. 358–366 (2008)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Jabbour, S., Ma, Y., Raddaoui, B., Sais, L.: Quantifying conflicts in propositional logic through prime implicates. Int. J. Approximate Reasoning 89, 27–40 (2017)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. Ma, Y., Qi, G., Xiao, G., Hitzler, P., Lin, Z.: An anytime algorithm for computing inconsistency measurement. In: Proceedings of International Conference on Knowledge Science, Engineering and Management (KSEM), pp. 29–40 (2009)

    Chapter  Google Scholar 

  25. Martinez, M.V., Pugliese, A., Simari, G.I., Subrahmanian, V.S., Prade, H.: How dirty is your relational database? An axiomatic approach. In: Proceedings of European Conference Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), pp. 103–114 (2007)

    Google Scholar 

  26. McAreavey, K., Liu, W., Miller, P.C.: Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases. Int. J. Approximate Reasoning 55(8), 1659–1693 (2014)

    Article  MathSciNet  Google Scholar 

  27. Mu, K., Jin, Z., Lu, R., Liu, W.: Measuring inconsistency in requirements specifications. In: Proceedings of European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), pp. 440–451 (2005)

    Google Scholar 

  28. Kedian, M., Liu, W., Jin, Z., Bell, D.A.: A syntax-based approach to measuring the degree of inconsistency for belief bases. Int. J. Approximate Reasoning 52(7), 978–999 (2011)

    Article  MathSciNet  Google Scholar 

  29. Parisi, F., Grant, J.: Knowledge representation in probabilistic spatio-temporal knowledge bases. J. Artif. Intell. Res. 55, 743–798 (2016)

    Article  MathSciNet  Google Scholar 

  30. Parisi, F., Grant, J.: On repairing and querying inconsistent probabilistic spatio-temporal databases. Int. J. Approximate Reasoning 84, 41–74 (2017)

    Article  MathSciNet  Google Scholar 

  31. Parisi, F., Grant, J.: Inconsistency measures for relational databases. CoRR, abs/1904.03403 (2019)

    Google Scholar 

  32. Parisi, F., Park, N., Pugliese, A., Subrahmanian, V.S.: Top-k user-defined vertex scoring queries in edge-labeled graph databases. ACM Trans. Web (TWEB) 12(4), 211–2135 (2018)

    Google Scholar 

  33. Robinson, I., Webber, J., Eifrem, E.: Graph Databases. O’Reilly Media Inc., Sebastopol (2013)

    Google Scholar 

  34. Thimm, M.: On the expressivity of inconsistency measures. Artif. Intell. 234, 120–151 (2016)

    Article  MathSciNet  Google Scholar 

  35. Thimm, M.: Stream-based inconsistency measurement. Int. J. Approximate Reasoning 68, 68–87 (2016)

    Article  MathSciNet  Google Scholar 

  36. Thimm, M., Wallner, J.P.: On the complexity of inconsistency measurement. Artif. Intell. 275, 411–456 (2019)

    Article  MathSciNet  Google Scholar 

  37. Vardi, M.Y.: The complexity of relational query languages (extended abstract). In Proceedings of Symposium on Theory of Computing (STOC), pp. 137–146 (1982)

    Google Scholar 

  38. Xiao, G., Ma, Y.: Inconsistency measurement based on variables in minimal unsatisfiable subsets. In Proceedings of 20th European Conference on Artificial Intelligence (ECAI), pp. 864–869 (2012)

    Google Scholar 

  39. Zhang, X., Wang, K., Wang, Z., Ma, Y., Qi, G., Feng, Z.: A distance-based framework for inconsistency-tolerant reasoning and inconsistency measurement in dl-lite. Int. J. Approximate Reasoning 89, 58–79 (2017)

    Article  MathSciNet  Google Scholar 

  40. Zhou, L., Huang, H., Qi, G., Ma, Y., Huang, Z., Qu, Y.: Measuring inconsistency in dl-lite ontologies. In: Proceedings of International Conference on Web Intelligence (WI), pp. 349–356 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Maryland at College Park, College Park, USA

    John Grant

  2. DIMES Department, University of Calabria, Rende, Italy

    Francesco Parisi

Authors
  1. John Grant
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco Parisi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francesco Parisi .

Editor information

Editors and Affiliations

  1. CNRS, University of Toulouse, Toulouse, France

    Andreas Herzig

  2. University of Helsinki, Helsinki, Finland

    Juha Kontinen

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Grant, J., Parisi, F. (2020). Measuring Inconsistency in a General Information Space. In: Herzig, A., Kontinen, J. (eds) Foundations of Information and Knowledge Systems. FoIKS 2020. Lecture Notes in Computer Science(), vol 12012. Springer, Cham. https://doi.org/10.1007/978-3-030-39951-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-39951-1_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-39950-4

  • Online ISBN: 978-3-030-39951-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation