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Title:Cross Domain Mathematical Concept Formation
Authors: Graham Steel ; Simon Colton ; Alan Bundy ; Toby Walsh
Date:May 2000
Publication Title:Procs of AISB'00 Symposium on Creative and Cultural Aspects of AI and Cognitive Science
Publication Type:Conference Paper
Abstract:
Many interesting concepts in mathematics are essentially "cross-domain" in nature, relating objects from more than one area of mathematics, e.g. prime order groups. These concepts are often vital to the formation of a mathematical theory. Often, the introduction of cross-domain concepts to an investigation seems to exercise a mathematician's creative ability. The HR program, (Colton, 1999), proposes new concepts in mathematics. Its original implementation was limited to working in one mathematical domain at a time, so it was unable to create cross-domain concepts. Here, we describe an extension of HR to multiple domains. Cross-domain concept formation is facilitated by generalisation of the data structures and heuristic measures employed by the program, and the implementation of a new production rule. Results achieved include generation of the concepts of prime order groups, graph nodes of maximal degree and an interesting class of graph.
Copyright:
2000 by The University of Edinburgh. All Rights Reserved
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No links available
Bibtex format
@InProceedings{EDI-INF-RR-0019,
author = { Graham Steel and Simon Colton and Alan Bundy and Toby Walsh },
title = {Cross Domain Mathematical Concept Formation},
book title = {Procs of AISB'00 Symposium on Creative and Cultural Aspects of AI and Cognitive Science},
year = 2000,
month = {May},
}


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