Learning Function-Free Horn Expressions

  • Authors:

  • Roni Khardon

  • Affiliations:

  • Division of Informatics,University of Edinburgh, The King‘s Buildings, Edinburgh EH9 3JZ, Scotland. roni@dcs.ed.ac.uk

  • Venue:
  • Machine Learning - The Eleventh Annual Conference on computational Learning Theory
  • Year:
  • 1999

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Abstract

The problem of learninguniversally quantified function freefirst order Horn expressions is studied.Several models of learning from equivalence and membership queriesare considered, including the model where interpretations are examples(Learning from Interpretations), the model where clauses are examples (Learning from Entailment), models where extensional or intentional background knowledge is given to the learner (as done in InductiveLogic Programming), and the model where the reasoning performance ofthe learner rather than identification is of interest(Learning to Reason). We present learning algorithms for all these tasks for the class ofuniversally quantified function free Horn expressions. The algorithms are polynomial in the number of predicate symbols inthe language and the number of clauses in the target Horn expressionbut exponential in the arity of predicates and the number ofuniversally quantified variables.We also provide lower bounds for these tasks by way of characterisingthe VC-dimension of this class of expressions.The exponential dependence on the number of variables isthe main gap between the lower and upper bounds.