Component-based Knowledge Spaces in Problem Solving and Inductive Reasoning

Two principles for component-based problem construction and ordering are presented and applied to different knowledge domains. The first principle is called “set inclusion.” It is used for constructing and ordering a set of chess problems. The second principle is “componentwise ordering of product sets.” We apply it in the domain of inductive reasoning (i.e. number-series completion). While set inclusion did not prove to be adequate for an application in the considered domain, the componentwise ordering of product sets led to remarkably good results in two empirical investigations.