That colloquium looked nice, I assume no slides are available? Barker is anouncing another seminar on deep learning and semantics, that looks intriguing from the attached public materials. I think that compsci furnishes ideas from formal language parsing that can be toy models of fragments of natural languages, Montague made a case in favour of formalizability. Wadler investigated monadic parsing and this can be an entry point for what is happening in linguistics. I have as reference arXiv:cs/0205026v1

added: on Barker seminar day 4 I see CCG derivations that are a close formalism of pregroup grammars used in the original post, nice to see this concurrently with nnets talk.