Theory Revision with Queries: DNF Formulas

  • Authors:
  • Judy Goldsmith;Robert H. Sloan;György Turán

  • Affiliations:
  • Department of Computer Science, University of Kentucky, 763 Anderson Hall, Lexington, KY 40506, USA. goldsmit@cs.uky.edu;Department of Computer Science, University of Illinois at Chicago, and National Science Foundation. sloan@uic.edu;Math, Stat., & Computer Science Department, University of Illinois at Chicago, Research Group on AI of Hungarian Academy of Sciences at University of Szeged. gyt@uic.edu

  • Venue:
  • Machine Learning
  • Year:
  • 2002

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Abstract

The theory revision, or concept revision, problem is to correct a given, roughly correct concept. This problem is considered here in the model of learning with equivalence and membership queries. A revision algorithm is considered efficient if the number of queries it makes is polynomial in the revision distance between the initial theory and the target theory, and polylogarithmic in the number of variables and the size of the initial theory. The revision distance is the minimal number of syntactic revision operations, such as the deletion or addition of literals, needed to obtain the target theory from the initial theory. Efficient revision algorithms are given for three classes of disjunctive normal form expressions: monotone k-DNF, monotone m-term DNF and unate two-term DNF. A negative result shows that some monotone DNF formulas are hard to revise.