On the hyperintensionality of relevant logics and some of their rivals

In this article, we present a definition of hyperintensionality appropriate to relevant logics. We then show that relevant logics are hyperintensional in this sense, drawing consequences for other non-classical logics, including $${\sf HYPE}$$ and some substructural logics. We further prove some positive and negative results concerning extensionality and hyperintensionality in relevant logics. We close by discussing related concepts for classifying formula contexts and potential applications of these results in the area of epistemic logic.