Journal of Philosophical Logic

, Volume 41, Issue 3, pp 595–612 | Cite as

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


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.


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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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Jc Beall
    • 1
    • 2
  • Ross Brady
    • 3
  • J. Michael Dunn
    • 4
  • A. P. Hazen
    • 5
    • 6
  • Edwin Mares
    • 7
  • Robert K. Meyer
    • 8
  • Graham Priest
    • 6
    • 9
    • 10
  • Greg Restall
    • 6
  • David Ripley
    • 6
  • John Slaney
    • 8
  • Richard Sylvan
    • 8
  1. 1.University of ConnecticutStorrsUSA
  2. 2.University of OtagoOtagoNew Zealand
  3. 3.La Trobe UniversityMelbourneAustralia
  4. 4.Indiana UniversityBloomingtonUSA
  5. 5.University of AlbertaAlbertaCanada
  6. 6.University of MelbourneParkvilleAustralia
  7. 7.Victoria University of WellingtonWellingtonNew Zealand
  8. 8.Australian National UniversityCanberraAustralia
  9. 9.Graduate CenterCity University of New YorkNew YorkUSA
  10. 10.University of St AndrewsFifeUK

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