A New Algorithmic Decision for Categorical Syllogisms via Caroll's Diagrams

TL;DR

This paper introduces SLCD, a diagram-based calculus system for categorical syllogisms, with an effective algorithm to determine reasoning validity that is accessible without specialized knowledge.

Contribution

It presents a formal diagrammatic calculus for syllogisms and an algorithm for validity checking that is simple and does not require expert understanding.

Findings

SLCD is closed under syllogistic inference.

The algorithm effectively determines syllogistic validity.

SLCD combines bilateral and trilateral diagrams for reasoning.

Abstract

In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and show that they are closed under the syllogistic criterion of inference which is the deletion of middle term. Therefore, it is implemented to let the formalism comprise synchronically bilateral and trilateral diagrammatical appearance and a naive algorithmic nature. And also, there is no need specific knowledge or exclusive ability to understand as well as to use it. Consequently, we give an effective algorithm used to determine whether a syllogistic reasoning valid or not by using SLCD.