On the Ternary Relation and Conditionality. Beall, J., Brady, R., Dunn, J., Hazen, A. P., Mares, E., Meyer, R., Priest, G., Restall, G., Ripley, D., Slaney, J., & Sylvan, R. Journal of Philosophical Logic, 41(3):595-612, 2012.
On the Ternary Relation and Conditionality [link]Web  abstract   bibtex   
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.
@article{ BeallBradyDunnHazenMaresMeyerPriestRestallRipleySlaneySylvan2012a,
  author = {Beall, Jc and Brady, Ross and Dunn, J. and Hazen, A. P. and Mares,
	Edwin and Meyer, Robert and Priest, Graham and Restall, Greg and
	Ripley, David and Slaney, John and Sylvan, Richard},
  title = {On the Ternary Relation and Conditionality},
  journal = {Journal of Philosophical Logic},
  year = {2012},
  volume = {41},
  pages = {595-612},
  number = {3},
  abstract = {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.},
  keywords = {SEMANTICS CONDITIONALS (Logic) CONCEPTS MODALITY (Logic) MATHEMATICS
	PHILOSOPHY TERNARY system Conditionality Conditionals Modal logics
	Possible worlds Relative relative possibility Routley-Meyer semantics
	Situations Ternary relation Ternary-relation semantics},
  urlweb = {http://dx.doi.org/10.1007/s10992-011-9191-5}
}

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