Alan M. Frisch, C. David Page Jr.
This paper studies sorted generalization-the generalization, with respect to an arbitrary taxonomic theory, of atomic formulas containing sorted variables. It develops an algorithm for the task, discusses the algorithm and task complexity, and presents semantic properties of sorted generalization. Based on its semantic properties, we show how sorted generalization is applicable to such problems as abduction, induction, knowledge base vivification, and analogical reasoning. Significant distinctions between this work and related work with taxonomic information arise from the generality of the taxonomic theories we allow, which may be any first-order taxonomic theories, and the semantic completeness properties of sorted generalization.