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.
翻译:作者近期在泛代数的一般框架中引入了抽象代数框架下的类比比例与相似性。本文旨在通过用相似性来形式化类比比例,从而在二者之间架起一座桥梁。这种基于相似性的方法之优势在于,比例与相似性之间的关联被内置于框架之中,因此显而易见——这颇具吸引力,因为比例与相似性均处于类比之核心;此外,未来关于相似性的研究成果可直接应用于类比比例。