Similarity preservation in default logic

  • Authors:

  • Rachel Ben-Eliyahu-Zohary;Nissim Francez;Michael Kaminski

  • Affiliations:

  • Department of Communication Systems Engineering, Ben Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel;Department of Computer Science, Technion – Israel Institute of Technology, Haifa 32000, Israel;Department of Computer Science, Technion – Israel Institute of Technology, Haifa 32000, Israel

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 1999

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Abstract

The paper identifies a problem in default reasoning in Reiter’s Default Logic and related systems: elements which are similar given the axioms only, become distinguishable in extensions. We explain why, sometimes, this is considered undesirable. Two approaches are presented for guaranteeing similarity preservation: One approach formalizes a way of uniformly applying the defaults to all similar elements by introducing generic extensions, which depend only on similarity types of objects. According to the second approach, for a restricted class of default theories, a default theory is viewed as a “shorthand notation” to what is “really meant” by its formulation. In this approach we propose a rewriting of defaults in a form that guarantees similarity preservation of the modified theory. It turns out that the above two approaches yield the same result.