“Information Flow and Relevant Logic,” in Logic, Language and Computation: The 1994 Moraga Proceedings, Jerry Seligman and Dag Westerståhl (editors) CSLI Press, 1995, pages 463–477.
John Perry, one of the two founders of the field of situation semantics, indicated in an interview in 1986 that there is some kind of connection between relevant logic and situation semantics.
I do know that a lot of ideas that seemed off the wall when I first encountered them years ago now seem pretty sensible. One example that our commentators don’t mention is relevance logic; there are a lot of themes in that literature that bear on the themes we mention.
In 1992, in Entailment volume 2, Nuel Belnap and J. Michael Dunn hinted at similar ideas. Referring to situation semantics, they wrote
… we do not mean to claim too much here. The Barwise-Perry semantics is clearly independent and its application to natural-language constructions is rich and novel. But we like to think that at least first degree (relevant) entailments have a home there.
In this paper I show that these hints and gestures are true. And perhaps truer than those that made them thought at the time. In this paper I introduce the semantics of relevant logics, then I will sketch the parts of situation theory relevant to our enterprise. Finally, I bring the two together in what is hopefully, a harmonious way.