论文标题
比例
Proportoids
论文作者
论文摘要
类比比例是``$ a $ a $ to $ b $ of $ c $ to $ d $''的表达式的表达。本文为二十年前的伊夫·莱普奇（Yves Lepage）发起的公理传统中类比比例的数学基础做出了贡献。为此，我们引入了比例，作为具有4个Ary类似比例关系$ a：b :: c：c：d $满足合适的公理并研究不同类型的比例映射映射和关系及其属性及其属性的集合。
Analogical proportions are expressions of the form ``$a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning. This paper contributes to the mathematical foundations of analogical proportions in the axiomatic tradition as initiated by Yves Lepage two decades ago. For this we introduce proportoids as sets endowed with a 4-ary analogical proportion relation $a:b::c:d$ satisfying a suitable set of axioms and study different kinds of proportion-preserving mappings and relations and their properties.
