What is relevance logic?

Arnon Avron

doi:10.1016/j.apal.2013.07.004

What is relevance logic?

Arnon Avron^*

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We suggest two precise abstract definitions of the notion of 'relevance logic' which are both independent of any proof system or semantics. We show that according to the simpler one, R→¬ (the intensional fragment of R) is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second (more complicated) definition, while all fragments of linear logic are not.

Original language	English
Pages (from-to)	26-48
Number of pages	23
Journal	Annals of Pure and Applied Logic
Volume	165
Issue number	1
DOIs	https://doi.org/10.1016/j.apal.2013.07.004
State	Published - Jan 2014

Keywords

Connectives
Entailment relations
Linear logic
Relevance logics

Access to Document

10.1016/j.apal.2013.07.004

Cite this

@article{6a2ca5e2e7d24d0bac9bbe4eccbcd53f,

title = "What is relevance logic?",

abstract = "We suggest two precise abstract definitions of the notion of 'relevance logic' which are both independent of any proof system or semantics. We show that according to the simpler one, R→¬ (the intensional fragment of R) is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second (more complicated) definition, while all fragments of linear logic are not.",

keywords = "Connectives, Entailment relations, Linear logic, Relevance logics",

author = "Arnon Avron",

year = "2014",

month = jan,

doi = "10.1016/j.apal.2013.07.004",

language = "אנגלית",

volume = "165",

pages = "26--48",

journal = "Annals of Pure and Applied Logic",

issn = "0168-0072",