Implicational F-structures and implicational relevance logics

A. Avron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and proof-theoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all elements except one are designated. Proof-theoretically they correspond to cut-free hypersequential Gentzen-type calculi. Another major property of all these logics is that the classical implication can faithfully be translated into them.

Original languageEnglish
Pages (from-to)788-802
Number of pages15
JournalJournal of Symbolic Logic
Volume65
Issue number2
DOIs
StatePublished - Jun 2000

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