  For example, suppose that \(\odot\alpha\) is \(\alpha {\rightarrow}\pi\). Then in order for \(\odot\) to obey DI, it would have to be the case that \(\alpha \vdash _{\mathcal{T}} (\alpha {\rightarrow}\pi) {\rightarrow}\pi\). That principle is violated by a number of non-classical theories for which \(\odot\), when defined  this way, does qualify as a Curry  connective.[28] 