LEG Networks for Ranking Functions

  • Christian Eichhorn
  • Gabriele Kern-Isberner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8761)


When using representations of plausibility for semantical frameworks, the storing capacity needed is usually exponentially in the number of variables. Therefore, network-based approaches that decompose the semantical space have proven to be fruitful in environments with probabilistic information. For applications where a more qualitative information is preferable to quantitative information, ordinal conditional functions (OCF) offer a convenient methodology. Here, Bayesian-like networks have been proposed for ranking functions, so called OCF-networks. These networks not only suffer from similar problems as Bayesian networks, in particular, allowing only restricted classes of conditional relationships, it also has been found recently that problems with admissibility may arise. In this paper we propose LEG networks for ranking functions, also carrying over an idea from probabilistics. OCF-LEG networks can be built for any conditional knowledge base and filled by local OCF that can be found by inductive reasoning. A global OCF is set up from the local ones, and it is shown that the global OCF is admissible with respect to the underlying knowledge base.


Knowledge Base Directed Acyclic Graph Consistency Condition Ranking Function Belief Revision 
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.


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  1. 1.
    Beierle, C., Hermsen, R., Kern-Isberner, G.: Observations on the Minimality of Ranking Functions for Qualitative Conditional Knowledge Bases and their Computation. In: Proceedings of the 27th International FLAIRS Conference, FLAIRS’27 (2014)Google Scholar
  2. 2.
    Benferhat, S., Dubois, D., Garcia, L., Prade, H.: On the transformation between possibilistic logic bases and possibilistic causal networks. International Journal of Approximate Reasoning 9(2), 135–173 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Benferhat, S., Tabia, K.: Belief Change in OCF-Based Networks in Presence of Sequences of Observations and Interventions: Application to Alert Correlation. In: Zhang, B.-T., Orgun, M.A. (eds.) PRICAI 2010. LNCS, vol. 6230, pp. 14–26. Springer, Heidelberg (2010)Google Scholar
  4. 4.
    de Finetti, B.: Theory of Probability, vol. 1, 2. John Wiley and Sons, New York (1974)zbMATHGoogle Scholar
  5. 5.
    Eichhorn, C., Kern-Isberner, G.: Using inductive reasoning for completing OCF-networks (2013) (submitted)Google Scholar
  6. 6.
    Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artificial Intelligence 84(1-2), 57–112 (1996)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  8. 8.
    Kern-Isberner, G., Eichhorn, C.: Intensional combination of rankings for OCF-networks. In: Boonthum-Denecke, C., Youngblood, M. (eds.) Proceedings of the 26th International FLAIRS Conference FLAIRS-2013, pp. 615–620. AAAI Press (2013)Google Scholar
  9. 9.
    Kern-Isberner, G., Eichhorn, C.: Structural inference from conditional knowledge bases. In: Unterhuber, M., Schurz, G. (eds.) Studia Logica Special Issue Logic and Probability: Reasoning in Uncertain Environments, vol. 102 (4), Springer Science+Business Media, Dordrecht (2014)Google Scholar
  10. 10.
    Lemmer, J.F.: Efficient minimum information updating for bayesian inferencing in expert systems. In: Proc. of the National Conference on Artificial Intelligence, AAAI 1982 (1982)Google Scholar
  11. 11.
    Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 35–110. Oxford University Press, Inc., New York (1994)Google Scholar
  12. 12.
    Meyer, C.-H.: Korrektes Schließen bei unvollständiger Information: Anwendung des Prinzips der maximalen Entropie in einem probabilistischen Expertensystem. 41. Peter Lang Publishing, Inc. (1998)Google Scholar
  13. 13.
    Pearl, J.: Probabilistic reasoning in intelligent systems – networks of plausible inference. Morgan Kaufmann (1989)Google Scholar
  14. 14.
    Pearl, J.: System Z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning. In: Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning About Knowledge, TARK 1990, pp. 121–135. Morgan Kaufmann Publishers Inc., San Francisco (1990)Google Scholar
  15. 15.
    Spohn, W.: The Laws of Belief: Ranking Theory and Its Philosophical Applications. Oxford University Press (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christian Eichhorn
    • 1
  • Gabriele Kern-Isberner
    • 1
  1. 1.Lehrstuhl Informatik 1Technische Universität DortmundDortmundGermany

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