Teaching Le\'sniewski's Prothetic with a Natural Deduction System

TL;DR

This paper introduces a natural deduction system for Leśniewski's protothetic, making it more accessible for students by replacing the complex axiomatic version with an intuitive deduction-based approach.

Contribution

It presents a novel natural deduction system for protothetic, facilitating easier understanding and teaching of Leśniewski's logic to students familiar with natural deduction methods.

Findings

The system simplifies the learning process for protothetic.

It demonstrates the applicability of natural deduction to complex propositional systems.

Enhances pedagogical approaches for teaching metalogic.

Abstract

Protothetic is one of the most stimulating systems for propositional logic. Including quantifiers and an inference rule for definitions, it is a very interesting mean for the study of many questions of metalogic. Unfortunately, it only exists in an axiomatic version, far too complicated and unusual to be easily understood by nowadays students in logic. In this paper, we present a system which is a natural deduction (in Fitch-Ja\'skowski's style) version of protothetic. According to us, this system is adequate for teaching Le\'sniewski's logic to students accustomed to natural deduction.