A Classification of Improper Inference Rules

Katsumi Sasaki

doi:10.18778/0138-0680.2022.12

Authors

Katsumi Sasaki Nanzan University, Faculty of Science and Technology, 18 Yamazato-Cho

DOI:

https://doi.org/10.18778/0138-0680.2022.12

Keywords:

sequent system, improper inference rule, natural deduction

Abstract

In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper as opposed to proper ones. Improper inference rules are more complicated than proper ones and more difficult to understand. In 2022, we provided a sequent system based solely on the application of proper rules. In the present paper, on the basis of our system from 2022, we classify improper inference rules.

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