CAN A VECTOR-SPACE BASED LEARNING-MODEL DISCOVER INDUCTIVE CLASS GENERALIZATION IN A SYMBOLIC ENVIRONMENT

We outline a general framework for inductive learning based on the rec ently proposed evolving transformation system model. Mathematical foun dations of this framework include two basic components: a set of opera tions (on objects) and the corresponding geometry defined by means of these operations, According to the framework, to perform inductive lea rning in a symbolic environment, the set of operations (class features ) may need to be dynamically updated, and this requires that the geome tric component allows for an evolving topology. In symbolic systems, a s defined in this paper, the geometric component allows for a dynamic change in topology, whereas finite-dimensional numeric systems (vector spaces) can essentially have only one natural topology, This face sho uld form the basis of a complete formal proof that, in a symbolic sett ing, the vector space based models, e. g. artificial neural networks, cannot capture inductive generalization. Since the presented argument indicates that the symbolic learning process is more powerful than the numeric process, it appears that only the former should be properly c alled an inductive learning process.