Logic-based analogical proportions

TL;DR

This paper extends an algebraic framework for analogical proportions to first-order logic, maintaining key properties and establishing new theoretical results in a more expressive logical setting.

Contribution

It introduces a first-order logic-based framework for analogical proportions, building on previous algebraic approaches and proving new properties in this richer setting.

Findings

Preserves desired properties of the algebraic framework

Extends the framework to full first-order logic

Proves novel theoretical results in the extended setting

Abstract

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.