Desiderata for Generalization-to-N Algorithms

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-toN algorithms. In the paper, we rst motivate and deene these desiderata, then review one of several alternative frameworks for generalizing number: an automata-based approach rst described in Cohen, 1988]. Finally, we describe a generalization-toN 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-toN .