What is relevance logic?

Arnon Avron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)26-48
Number of pages23
JournalAnnals of Pure and Applied Logic
Issue number1
StatePublished - Jan 2014


  • Connectives
  • Entailment relations
  • Linear logic
  • Relevance logics


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