The Consistency of the CADIAG-2 Knowledge Base: A Probabilistic Approach

  • Pavel Klinov
  • Bijan Parsia
  • David Picado-Muiño
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


The paper presents the methodology and the results of checking consistency of the knowledge base of CADIAG-2, a large-scale medical expert system. Such knowledge base consists of a large collection of rules representing knowledge about various medical entities (symptoms, signs, diseases...) and relationships between them. The major portion of the rules are uncertain, i.e., they specify to what degree a medical entity is confirmed by another medical entity or a combination of them. Given the size of the system and the uncertainty it has been challenging to validate its consistency. Recent attempts to partially formalise CADIAG-2’s knowledge base into decidable Gödel logics have shown that, on that formalisation, CADIAG-2 is inconsistent. In this paper we verify this result with an alternative, more expressive formalisation of CADIAG-2 as a set of probabilistic conditional statements and apply a state-of-the-art probabilistic logic solver to determine satisfiability of the knowledge base and to extract conflicting sets of rules. As CADIAG-2 is too large to be handled out of the box we describe an approach to split the knowledge base into fragments that can be tested independently and prove that such methodology is complete (i.e., is guaranteed to find all conflicts). With this approach we are able to determine that CADIAG-2 contains numerous sets of conflicting rules and compute all of them for a slightly relaxed version of the knowledge base.


Knowledge Base Description Logic Column Generation Medical Entity Propositional Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adlassnig, K., Kolarz, G., Scheithauer, W., Grabner, H.: Approach to a hospital-based application of a medical expert system. Informatics for Health and Social Care 11(3), 205–223 (1986)Google Scholar
  2. 2.
    Adlassnig, K., Kolarz, G., Effenberger, W., Grabner, H.: Cadiag: Approaches to computer-assisted medical diagnosis. Computers in Biology and Medicine 15, 315–335 (1985)CrossRefGoogle Scholar
  3. 3.
    Adlassnig, K.: Fuzzy set theory in medical diagnosis. IEEE Transactions on Systems, Man and Cybernetics 16(2), 260–265 (1986)CrossRefGoogle Scholar
  4. 4.
    Leitich, H., Adlassnig, K., Kolarz, G.: Evaluation of two different models of semiautomatic knowledge acquisition for the medical consultant system CADIAG-2/RHEUMA. Artificial Intelligence in Medicine 25, 215–225 (2002)CrossRefGoogle Scholar
  5. 5.
    Ciabattoni, A., Vetterlein, T.: On the fuzzy (logical) content of Cadiag2. Fuzzy Sets and Systems (2009) (to appear shortly)Google Scholar
  6. 6.
    Picado Muiño, D.: The (probabilistic) logical content of cadiag2. In: Proceedings of ICAART 2010, pp. 28–35 (2010)Google Scholar
  7. 7.
    Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Zadeh, L.: Fuzzy logic and approximate reasoning. Synthese 30, 407–428 (1975)CrossRefzbMATHGoogle Scholar
  9. 9.
    Klir, G., Folger, T.: Fuzzy Sets, Uncertainty and Information. Prentice-Hall International, Englewood Cliffs (1988)zbMATHGoogle Scholar
  10. 10.
    Zimmermann, H.: Fuzzy Set Theory and its Applications. Kluwer Academic Publisher, Dordrecht (1991)CrossRefzbMATHGoogle Scholar
  11. 11.
    Ciabattoni, A., Rusnok, P.: On the classical content of monadic G~ and its applications to a fuzzy medical expert system. In: Proceedings of the 12th International Conference on the Principles of Knowledge Representation and Reasoning (2010)Google Scholar
  12. 12.
    Klinov, P., Parsia, B.: Pronto: A practical probabilistic description logic reasoner. In: International Workshop on Uncertainty in Description Logics (2010)Google Scholar
  13. 13.
    Hooker, J.N.: Quantitative approach to logical reasoning. Decision Support Systems 4, 45–69 (1988)CrossRefGoogle Scholar
  14. 14.
    Baader, F., Calvanese, D., McGuiness, D., Nardi, D., Patel-Schneider, P.F.: Description Logic Handbook. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  15. 15.
    Horridge, M., Parsia, B., Sattler, U.: Laconic and precise justifications in OWL. In: Sheth, A.P., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 323–338. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32, 57–95 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Parker, M., Ryan, J.: Finding the minimum weight IIS cover of an infeasible system of linear inequalities. Ann. Math. Artif. Intell. 17(1-2), 107–126 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Moser, W., Adlassnig, K.: Consistency checking of binary categorical relationships in a medical knowledge bases. Artificial Intelligence in Medicine 8, 389–407 (1992)CrossRefGoogle Scholar
  19. 19.
    Gabbay, D.M., Hunter, A.: Making inconsistency respectable: a logical framework for inconsistency in reasoning. In: Jorrand, P., Kelemen, J. (eds.) FAIR 1991. LNCS, vol. 535, pp. 19–32. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  20. 20.
    Sattler, U., Schneider, T., Zakharyaschev, M.: Which kind of module should I extract? In: Grau, B.C., Horrocks, I., Motik, B., Sattler, U. (eds.) Description Logics. CEUR Workshop Proceedings,, vol. 477 (2009)Google Scholar
  21. 21.
    Cuenca Grau, B., Horrocks, I., Kazakov, Y., Sattler, U.: Extracting modules from ontologies: A logic-based approach. In: Stuckenschmidt, H., Parent, C., Spaccapietra, S. (eds.) Modular Ontologies. LNCS, vol. 5445, pp. 159–186. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Cuenca Grau, B., Parsia, B., Sirin, E.: Ontology integration using ε-connections. In: Stuckenschmidt, H., Parent, C., Spaccapietra, S. (eds.) Modular Ontologies. LNCS, vol. 5445, pp. 293–320. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pavel Klinov
    • 1
  • Bijan Parsia
    • 1
  • David Picado-Muiño
    • 2
  1. 1.University of ManchesterManchesterUK
  2. 2.Institut für Diskrete Mathematik und GeometrieViennaAustria

Personalised recommendations