*Jude W. Shavlik, Gerald F. DeJong*

This paper addresses the important issue in explanation-based learning of generalizing number. Most research in explanation-based learning involves relaxing constraints on the variables in an explanation, rather than generalizing the number of inference rules used. However, many concepts require generalizing the structure of the explanation. An explanation-based approach to the problem of generalizing to N is presented. The fully-implemented BAGGER system analyzes explanation structures and detects extendible repeated, inter-dependent applications of rules. When any are found, the explanation is extended is extended so that an arbitrary number of repeated applications of the original rule are supported. The final structure is then generalized and a new rule produced. An important property of the extended rules is that their preconditions are expressed in terms of the initial state - they do not depend on the results of intermediate applications of the original rule. To illustrate the approach, portions of several situation calculus examples from the blocks world are analyzed. The approach presented leads to the acquisition of efficient plans that can be used to clear an object directly supporting an arbitrary number of other objects, build towers of arbitrary height, and unstack towers containing any number of blocks.

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