Transformation Rules for First-Order Probabilistic Conditional Logic Yielding Parametric Uniformity

  • Ruth Janning
  • Christoph Beierle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7006)


A major challenge in knowledge representation is to express uncertain knowledge. One possibility is to combine logic and probability. In this paper, we investigate the logic FO-PCL that uses first-order probabilistic conditionals to formulate uncertain knowledge. Reasoning in FO-PCL employs the principle of maximum entropy which in this context refers to the set of all ground instances of the conditionals in a knowledge base \(\mathcal R\). We formalize the syntactic criterion of FO-PCL interactions in \(\mathcal R\) prohibiting the maximum entropy model computation on the level of conditionals instead of their instances. A set of rules is developed transforming \(\mathcal R\) into an equivalent knowledge base \(\mathcal R^{\prime}\) without FO-PCL interactions.


Maximum Entropy Transformation Rule Predicate Symbol Constant Symbol Ground Atom 
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  1. 1.
    Adams, E.W.: The Logic of Conditionals. D. Reidel Publishing Company, Dordrecht-Holland (1975)CrossRefzbMATHGoogle Scholar
  2. 2.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Berlin (1999)zbMATHGoogle Scholar
  3. 3.
    Fisseler, J.: Learning and Modeling with Probabilistic Conditional Logic. Dissertations in Artificial Intelligence, vol. 328. IOS Press, Amsterdam (2010)zbMATHGoogle Scholar
  4. 4.
    Getoor, L., Taskar, B. (eds.): Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)zbMATHGoogle Scholar
  5. 5.
    Halpern, J.Y.: Reasoning About Uncertainty. MIT Press, Cambridge (2005)zbMATHGoogle Scholar
  6. 6.
    Janning, R.: Transforming first-order probabilistic conditional logic knowledge bases to facilitate the maximum entropy model computation. Master’s thesis, FernUniversität in Hagen (to appear, 2011)Google 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., Thimm, M.: Novel Semantical Approaches to Relational Probabilistic Conditionals. In: Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2010), pp. 382–392 (May 2010)Google Scholar
  9. 9.
    Loh, S., Thimm, M., Kern-Isberner, G.: On the Problem of Grounding a Relational Probabilistic Conditional Knowledge Base. In: Proceedings of the 14th International Workshop on Non-Monotonic Reasoning (NMR 2010), Toronto, Canada (May 2010)Google Scholar
  10. 10.
    Nute, D., Cross, C.B.: Conditional logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 4, pp. 1–98. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  11. 11.
    Paris, J.B.: The uncertain reasoner’s companion - A mathematical perspective. Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  12. 12.
    Poole, D.: First-order probabilistic inference. In: Gottlob, G., Walsh, T. (eds.) Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence (IJCAI 2003), pp. 985–991. Morgan Kaufmann, San Francisco (2003)Google Scholar
  13. 13.
    Rödder, W., Kern-Isberner, G.: Representation and extraction of information by probabilistic logic. Information Systems 21(8), 637–652 (1996)CrossRefzbMATHGoogle Scholar
  14. 14.
    Thimm, M., Kern-Isberner, G., Fisseler, J.: Relational probabilistic conditional reasoning at maximum entropy. In: Liu, W. (ed.) ECSQARU 2011. LNCS, vol. 6717, pp. 447–458. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ruth Janning
    • 1
  • Christoph Beierle
    • 1
  1. 1.Fak. für Mathematik und InformatikFernUniversitätHagenGermany

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