Gentzen formulations of two positive relevance logics

Studia Logica 39 (4):381 - 403 (1980)
The author gentzenizes the positive fragmentsT + andR + of relevantT andR using formulas with, prefixes (subscripts). There are three main Gentzen formulations ofS +{T+,R +} calledW 1 S +,W 2 S + andG 2 S +. The first two have the rule of modus ponens. All of them have a weak rule DL for disjunction introduction on the left. DL is not admissible inS + but it is needed in the proof of a cut elimination theorem forG 2 S +.W 1 S + has a weak rule of weakeningW 1 and it is not closed under a general transitivity rule. This allows the proof that A inS + iff A inW 1 S +. From the cut elimination theorem forG 2 S + it follows that if A inS +, then A inG 2 S +. In order to prove the converse,W 2 S + is needed. It contains modus ponens, transitivity, and a restricted weakening rule.G 2 S + is contained inW 2 S + and there is a proof that A inW 2 S + iff A inW 1 S +.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF00713549
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,765
Through your library
References found in this work BETA

Add more references

Citations of this work BETA
Four Relevant Gentzen Systems.Steve Giambrone & Aleksandar Kron - 1987 - Studia Logica 46 (1):55 - 71.

Add more citations

Similar books and articles
Added to PP index

Total downloads
26 ( #216,943 of 2,214,577 )

Recent downloads (6 months)
1 ( #408,824 of 2,214,577 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature