Hyperintensionality for Logics

A logic is said to be hyperintensional when it admits connectives or operators creating hyperintensional contexts, i.e. sentential contexts not respecting the intersubstitutivity salva veritate of co-intensionals. Odintsov and Wansing (J Philos Logic 50(1):33-56, 2021) suggest a formal criterion for classifying a logic as hyperintensional based on whether its consequence relation is self-extensional. I argue that satisfaction of Odintsov and Wansing's criterion is neither necessary nor sufficient for characterising a logic as hyperintensional. Indeed, the criterion classifies as hyperintensional logics which are not meant to capture hyperintensional behaviour, and fails to classify as hyperintensional logics which admit some forms of hyperintensional behaviour. I suggest several possible criteria for a logic to count as hyperintensional, arguing that each of them corresponds to a different understanding of hyperintensionality for logics. Then, I weigh these criteria against a family of logics, which display different "nuances" of hyperintensional behaviour. Finally, I gesture towards a diagnosis of hyperintensionality for logics.