# Desiderata for generalization-to-N algorithms

## Abstract

Systems that perform “generalization-to-*N*” in explanation-based learning generalize a proof tree by generalizing the *shape* of the tree, rather than simply changing constants to variables. This paper introduces a formal framework which can be used either to characterize or to specify the outputs of an algorithm for generalizing number. The framework consists of two desiderata, or desired properties, for generalization-to-*N* algorithms. In the paper, we first motivate and define these desiderata, then review one of several alternative frameworks for generalizing number: an automata-based approach first described in [Cohen, 1988]. Finally, we describe a generalization-to -*N* technique that provably meets these desiderata. As an illustration of the operation of the new algorithm, an implementation of it is applied to a number of examples from the literature on generalization-to-*N*.

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