Aristotle' Relations: An Interpretation in Combinatory Logic

TL;DR

This paper proposes a novel approach to model Aristotle's relations using combinatory logic, extending traditional class-based syllogism models to include relational composition and logical connectives.

Contribution

It introduces a new calculus that incorporates relations and their composition within combinatory logic, bridging Aristotle's relational category with modern logical frameworks.

Findings

Models Aristotle's relations with combinatory logic

Includes composition of predicates with logical connectives

Extends traditional class-based syllogism models

Abstract

The usual modelling of the syllogisms of the Organon by a calculus of classes does not include relations. Aristotle may however have envisioned them in the first two books as the category of relatives, where he allowed them to compose with themselves. Composition is the main operation in combinatory logic, which therefore offers itself for a new kind of modelling. The resulting calculus includes also composition of predicates by logical connectives.