On the Tractability of Learning from Incomplete Theories

Abstract One well-known limitation of the explanation-based approach to concept learning is the need for a domain theory strong enough to deductively entail training examples of the concept. As such a theory may be unavailable in many situations, the problem of learning from incomplete domain theories must be addressed. The aim of this paper is to use the Valiant/Natarajan theoretical formalizations of concept learning to study the tractability of learning from incomplete domain theories. In particular, we present an in-depth analysis of the tractability of learning functions from determinations , a particular form of incomplete domain theory[3]. We show that only two of the five function families consistent with the five total determinations are polynomial-time learnable. We introduce the notion of “exceptions, and use it to identify sufficient conditions for the learnability of function families consistent with partial and extended determinations. While our results are specific to determinations, we believe that the underlying approach can be used to analyze other forms of incomplete theories.