The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. The purpose of this paper is to lift that framework from universal algebra to the strictly more expressive setting of full first-order logic. We show that the so-obtained logic-based framework preserves all desired properties and we prove novel results in that extended setting.
翻译:作者最近在通用代数的通用设定下引入了一个抽象的代数类比比例框架。本文的目的是将该框架从通用代数提升到表达能力严格更强的一阶完全逻辑设定中。我们证明如此获得的基于逻辑的框架保留了所有期望的性质,并在此扩展设定中证明了新的结果。