Similarity-based analogical proportions
This work addresses a theoretical gap in analogy research for AI and cognitive science, but it is incremental as it builds on existing algebraic frameworks.
The paper tackles the problem of connecting analogical proportions to similarity by formulating proportions in terms of similarity within an algebraic framework, resulting in a built-in connection that allows future similarity results to be directly applied to proportions.
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical proportions by formulating the latter in terms of the former. The benefit of this similarity-based approach is that the connection between proportions and similarity is built into the framework and therefore evident which is appealing since proportions and similarity are both at the center of analogy; moreover, future results on similarity can directly be applied to analogical proportions.