Boolean proportions

TL;DR

This paper explores boolean proportions within an algebraic framework, showing their equivalence to existing models and demonstrating the framework's robustness and broad applicability.

Contribution

It introduces a unified algebraic framework for boolean proportions that encompasses two prominent existing models, enhancing theoretical understanding.

Findings

Boolean proportions coincide with two established models.

The unified framework captures multiple modeling approaches.

Provides evidence for the framework's robustness and applicability.

Abstract

The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. This paper studies analogical proportions in the boolean domain consisting of two elements 0 and 1 within his framework. It turns out that our notion of boolean proportions coincides with two prominent models from the literature in different settings. This means that we can capture two separate modellings of boolean proportions within a single framework which is mathematically appealing and provides further evidence for the robustness and applicability of the general framework.