Related papers: Generalization-baed similarity

Generalization-baed similarity

URL: http://arxiv.org/abs/2302.10096v7
Date: Thu, 17 Oct 2024 17:48:29 GMT
Title: Generalization-baed similarity
Authors: Christian Antić,
Abstract summary: We develop an abstract notion of similarity based on the observation that sets of generalizations encode important properties of elements. We show that similarity defined in this way has appealing mathematical properties.
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Abstract: Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the observation that sets of generalizations encode important properties of elements. We show that similarity defined in this way has appealing mathematical properties. As we construct our notion of similarity from first principles using only elementary concepts of universal algebra, to convince the reader of its plausibility, we show that it can model fundamental relations occurring in mathematics and be naturally embedded into first-order logic via model-theoretic types.

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