 Care is needed so as to not conflate channel composition as specified above in  (14),  with the channel application specified above in  (12)  and  (13).  The latter involves feeding a channel its input, whereas the former involves the compositions of channels themselves. Tedder (2017) argues elegantly for the composition and application of information channels to be treated separately, and that we should not expect the properties of both (specified via structural rules on the ternary relation \(\mapsto\) to be the same. For arguments with regard to just what properties it is that we should expect channel composition and application to possess, see Tedder (2021) and Sequoiah-Grayson (2021). Sequoiah-Grayson (2010) argues that a basic theory of information flow with a semantics given by the Lambek calculi gives us an informational interpretation of the dynamic predicate logic (DPL) of Groenendijk and Stokhof (1991).