HR - Automatic Concept Formation in Finite Algebras

Simon Colton

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 infinite algebras, such as finite group theory. We first determined a reason for HR 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.

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