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Using Equivalences of Worlds for Aggregation Semantics of Relational Conditionals

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7526)

Abstract

For relational probabilistic conditionals, the so-called aggregation semantics has been proposed recently. Applying the maximum entropy principle for reasoning under aggregation semantics requires solving a complex optimization problem. Here, we improve an approach to solving this optimization problem by Generalized Iterative Scaling (GIS). After showing how the method of Lagrange multipliers can also be used for aggregation semantics, we exploit that possible worlds are structurally equivalent with respect to a knowledge base \(\mathcal R\) if they have the same verification and falsification properties. We present a GIS algorithm operating on the induced equivalence classes of worlds; its implementation yields significant performance improvements.

Keywords

  • Equivalence Class
  • Feature Function
  • Maximum Entropy
  • Relative Entropy
  • Ground Atom

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.

The research reported here was partially supported by the DFG (grant BE 1700/7-2).

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Finthammer, M., Beierle, C. (2012). Using Equivalences of Worlds for Aggregation Semantics of Relational Conditionals. In: Glimm, B., Krüger, A. (eds) KI 2012: Advances in Artificial Intelligence. KI 2012. Lecture Notes in Computer Science(), vol 7526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33347-7_5

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  • DOI: https://doi.org/10.1007/978-3-642-33347-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33346-0

  • Online ISBN: 978-3-642-33347-7

  • eBook Packages: Computer ScienceComputer Science (R0)