Deduction theorems for weak implicational logics
type: Item
instance of: scholarly article
title: Deduction theorems for weak implicational logics
zbMATH Open document ID: 0536.03001
DOI: 10.1007/BF00370338
published in: Studia Logica
publication date: 1982-01-01T00:00:00Z
review text: The standard deduction theorem or introduction rule for implication, for classical logic is also valid for intuitionistic logic, but just as with predicate logic, other rules of inference have to be restricted if the theorem is to hold for weaker implicational logics. In this paper the author looks in detail at special cases of the Gentzen rules for \(\vdash\) and shows that various subsets of these in effect constitute deduction theorems determining all the theorems of many well known as well as not well known implicational logics. In particular systems of rules are given which are equivalent to the relevance logics \(E_{\to}\), \(R_{\to}\), T, P-W and P-W-I.
Mathematics Subject Classification ID: 03B20
zbMATH DE Number: 3851042
zbMATH Keywords: weak implicational logics
zbMATH Keywords: Gentzen rules
zbMATH Keywords: deduction theorems
zbMATH Keywords: relevance logics
author: Martin W. Bunder
MaRDI profile type: Publication
cites work: Q5825229
cites work: Über Tautologien, in Welchen Keine Variable Mehr Als Zweimal Vorkommt
cites work: Positive logic and \(\lambda\)-constants
full work available at URL: https://doi.org/10.1007/bf00370338
OpenAlex ID: W1971424167
description: scientific article; zbMATH DE number 3851042