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

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.