A diagrammatic calculus of n-term syllogisms

TL;DR

This paper generalizes a diagrammatic calculus for syllogisms to n-term cases, demonstrating that valid syllogisms can be derived through calculation and linking the approach to rewriting systems and category theory.

Contribution

It introduces a comprehensive diagrammatic calculus for n-term syllogisms and connects it to rewriting systems and category theory frameworks.

Findings

Valid n-term syllogisms are those derivable by calculation.

The calculus is extended from previous work on simpler syllogisms.

Connections with rewriting systems and category theory are established.

Abstract

We extend the diagrammatic calculus of syllogisms introduced in our previous paper to the general case of n-term syllogisms, showing that the valid ones are exactly those whose conclusion follows by calculation. Moreover, by pointing out the existing connections with the theory of rewriting systems we will also single out a suitable category theoretic framework for the calculus.