An Algebraic Approach to Inductive Learning

The paper presents an approach to inductive machine learning based on a consistent integration of the generalization-based (such as inductive learning from examples) and metric-based (such asagglomerative clustering) approaches. The approach stems from the natural idea (formally studied within lattice theory) to estimate the similarity between two objects in a hierarchical structure by the distances to their closest common parent. The hierarchies used are subsumption lattices induced by generalization operatiors (e.g. lgg) commonly used in inductive learning. Using some results from the theory the paper defines a unified framework for solving basic inductive learning tasks. An algorithm for this purpose is proposed and its performance is illustrated by examples.