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<p>Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops <i>from the ground up</i> 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 can be naturally embedded into first-order logic via model-theoretic types. Finally, we sketch some potential applications to theoretical computer science and artificial intelligence.</p>

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Generalization-based similarity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月20日

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  • Christian Antić

摘要

Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops 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 can be naturally embedded into first-order logic via model-theoretic types. Finally, we sketch some potential applications to theoretical computer science and artificial intelligence.