Using Background Knowledge for AGM Belief Revision

  • Christian EichhornEmail author
  • Gabriele Kern-Isberner
  • Katharina Behring
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 349)


By using the concept of possible worlds as system states, it is possible to express a system’s internal state with the configuration of the system’s variables. In the same way, the (usually incomplete and not necessarily correct) belief of an intelligent agent about the system’s state can be expressed by a set of possible worlds. If this belief is to be changed due to more accurate information about the system’s true state, it is reasonable to incorporate the new information while at the same time abandon as little information as possible, that is, to minimally change the belief of the agent. In this paper we define semantical distances between possible worlds based on the background beliefs of an agent which are represented as a conditional knowledge base, by defining distances on the syntax of the (semantical) conditional structure. With these distances, we instantiate AGM belief change operators that incorporate new information into the belief state and implement the principle of minimal change by selecting a set of worlds that are closest to the actual beliefs. We demonstrate that using the background knowledge to calculate distances allows us to change the belief state of the agent in a way that is semantically more correct than using, e.g., Dalal’s distance. We finally discuss that defining the distances on a syntactical distance on conditional structures allows us to implement the resulting belief change operators more efficiently.



This work was supported by DFG-Grant KI1413/5-1 of Prof. Dr. Gabriele Kern-Isberner as part of the Priority Program “New Frameworks of Rationality” (SPP 1516). Christian Eichhorn is supported by this grant. Thanks to Richard Niland for his work on the implementation and for carefully proof-reading this paper.


  1. 1.
    Agrawal, Rakesh; Srikant, Ramakrishnan: Fast Algorithms for Mining Association Rules in Large Databases, in: Proceedings of the 20th International Conference on Very Large Data Bases VLDB ’94, 1994, pp. 487–499.Google Scholar
  2. 2.
    Alchourrón, Carlos E.; Gärdenfors, Peter; Makinson, David: On the logic of theory change: Partial meet contraction and revision functions, Journal of Symbolic Logic, vol 50, pp. 510–530.Google Scholar
  3. 3.
    Dalal, Mukesh: Investigations Into a Theory of Knowledge Base Revision: Preliminary Report, Mitchell, Tom M.; Smith, Reid G. (eds.): Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI-88), Cambridge, MA: MIT Press, 1988, pp. 475–479.Google Scholar
  4. 4.
    de Finetti, Bruno: Theory of Probability, New York: John Wiley & Sons, vols. 1, 2, 1974.Google Scholar
  5. 5.
    Diekmann, Katharina: Ähnlichkeitsbasierte Inferenzen für kontrafaktische Konditionale, Master’s Thesis Technische Universiät Dortmund, 2013.Google Scholar
  6. 6.
    Eichhorn, Christian; Kern-Isberner, Gabriele: LEG Networks for Ranking Functions, in: Fermé, Eduardo; Leite, João (eds.): Logics in Artificial Intelligence (Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA’14)), Springer International (Lecture Notes in Computer Science, vol. 8761) 2014, pp. 210–223.Google Scholar
  7. 7.
    Eichhorn, Christian; Kern-Isberner, Gabriele: Using inductive reasoning for completing OCF-networks, Journal of Applied Logic, vol. 13 (4, Part 2): Special Issue dedicated to Uncertain Reasoning at FLAIRS, 2015, pp. 605–627.Google Scholar
  8. 8.
    Gärdenfors, Peter; Rott, Hans: Belief Revision, in: Gabbay, Dov M.; Hogger, C. J.; Robinson, J. A. (eds.): Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 4, New York: Oxford University Press, 1994, pp. 35–132.Google Scholar
  9. 9.
    Gilio, Angelo: Probabilistic reasoning under coherence in system P\(^\star \), Annals of Mathematics and Artificial Intelligence vol. 34, 2002, pp. 5–34.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Goldszmidt, Moisés; Pearl, Judea: Qualitative probabilities for default reasoning, belief revision, and causal modeling, Artificial Intelligence, vol. 84 (1–2), 1996, pp. 57–112.Google Scholar
  11. 11.
    Hamming, R. W.: Error detecting and error correcting codes, The Bell System Technical Journal, vol. 29 (2) 1950, pp. 147–160.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Katsuno, Hirofumi; Mendelzon, Alberto O.: Propositional knowledge base revision and minimal change Artificial Intelligence, vol. 52 (3), 1991, pp. 263–294.Google Scholar
  13. 13.
    Kelley, J. L.: General Topology, New York: Van Nostrand, 1955.zbMATHGoogle Scholar
  14. 14.
    Kern-Isberner, Gabriele: Conditionals in Nonmonotonic Reasoning and Belief Revision – Considering Conditionals as Agents, Berlin: Springer Science+Business Media (Lecture Notes in Computer Science, Nr. 2087), 2001.Google Scholar
  15. 15.
    Kern-Isberner, Gabriele: A Thorough Axiomatization of a Principle of Conditional Preservation in Belief Revision, Annals of Mathematics and Artificial Intelligence, vol. 40 (1–2), 2004, pp. 127–164.Google Scholar
  16. 16.
    Lehmann, Daniel; Magidor, Menachem; Schlechta, Karl: Distance Semantics for Belief Revision, The Journal of Symbolic Logic, vol. 66 (1), 2001, pp. 295–317.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Thimm, Matthias: Tweety – A Comprehensive Collection of Java Libraries for Logical Aspects of Artificial Intelligence and Knowledge Representation, Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR’14), 2014.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Christian Eichhorn
    • 1
    Email author
  • Gabriele Kern-Isberner
    • 1
  • Katharina Behring
    • 2
  1. 1.Lehrstuhl Informatik 1Technische Universität DortmundDortmundGermany
  2. 2.Accenture PLM GmbHLeinfelden-EchterdingenGermany

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