HR - Automatic Concept Formation in Finite Algebras
نویسنده
چکیده
We are investigating how and why mathematicians invent new concepts while developing a theory, and implementing our ideas into the HR system, which automatically produces, assesses and displays concepts in finite algebras, such as finite group theory. We fit’st determined a reason for HI~ to produce concepts to classify a given set of groups up to isomorphism. Doing so would involve inventing concepts which help describe groups, so a classification can occur, and inventing concepts which help generate new examples of groups, so that improvements to the classification are necessitated, perpetuating the process. Next, we developed measures to tell us how interesting the concepts produced were (see Colton 1997). This helped us determine the kinds of concepts HR. should produce and with this in mind, we implemented production rules taking one (or two) concepts as input and outputting a new concept.
منابع مشابه
HR - A System for Machine Discovery in Finite Algebras
We describe the HR concept formation program which invents mathematical definitions and conjectures in finite algebras such as group theory and ring theory. We give the methods behind and the reasons for the concept formation in HR, an evaluation of its performance in its training domain, group theory, and a look at HR in domains other than group theory.
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