A Unified Interpretation of the Semantics of Relevance Logic

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I introduce a novel and quite intuitive interpretation of the ternary relation that figures in the relational semantics of many relevance logics. Conceptually, my interpretation makes use only of incompatibility and parthood relations, defined over a set of states. In this way, the proposed interpretation—of the ternary relation and the conditional—extends Dunn’s and Restall’s works on negation and the Routley star operator. Therefore, the interpretation is unified, and hence not only intuitive but also parsimonious. Additionally, the interpretation provides us with a cogent argument to the effect that a ternary relation is indispensable, and we cannot merely do with a binary relation.

Original languageAmerican English
Pages (from-to)1105-1125
Number of pages21
Issue number528
StatePublished - 1 Oct 2023

All Science Journal Classification (ASJC) codes

  • Philosophy


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