The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

MSc Thesis #9911

Title:Cross-Domain concept Formation Using HR
Date: 1999
Abstract:Many interesting and valuable concepts in mathematics are essentially `cross-domain' in nature, i.e. they relate objects, ideas and theories from more than one area of mathematics. Examples include prime order groups and graph nodes of maximal degree. These concepts are often involved in vital steps in the formation of a mathematical theory.The HR program, developed by Simon Colton at the University of Edinburgh, has achieved some success in proposing new concepts in mathematics. It functions by performing best-first heuristic search on the space of mathematical concepts. However, its original implementation was limited to working in a single mathematical domain at a time, and so was unable to create cross-domain concepts. In the work described here, the HR system was extended to multiple domains. Cross-domain concept formation was facilitated by way of modifications to the heuristic measures employed by the program, and implementation of a new production rule to spot extremal values. Results achieved include rediscovery of nodes of maximal degree and prime order groups, discovery of an interesting type of graph and a generally high yield of good quality concepts, as defined on a four point scale explained in this report. Suggestions are given at the end of the project for improving search control.

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