Four-valued semantics for relevant logics (and some of their rivals)

Greg Restall*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the 'Australian Plan' semantics, which uses a unary operator '{star operator}' for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a semantics for the contraction-free relevant logic C (or RW). Unfortunately, its approach seems to model little else. The third approach seems to capture a wide range of formal systems, but at the time of writing, lacks a completeness proof.

Original languageEnglish
Pages (from-to)139-160
Number of pages22
JournalJournal of Philosophical Logic
Volume24
Issue number2
DOIs
Publication statusPublished - Apr 1995

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