On the Ternary Relation and Conditionality

Jc Beall*, Ross Brady, J. Michael Dunn, A. P. Hazen, Edwin Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney, Richard Sylvan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.

Original languageEnglish
Pages (from-to)595-612
Number of pages18
JournalJournal of Philosophical Logic
Issue number3
Publication statusPublished - Jun 2012


  • Ternary relation
  • Ternary-relation semantics
  • Possible worlds
  • Situations
  • Modal logics
  • Paraconsistent logics
  • Relevant logics
  • Routley-Meyer semantics
  • Conditionals
  • Conditionality
  • Relative relative possibility


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