Over at the n-category café, John Baez and students have some ideas about using category theory for linguistics
https://johncarlosbaez.wordpress.com/2018/02/11/linguistics-using-category-theory/ for some notes on John Baez’ blog)
I do not understand a word of what they’re saying, just wanted to put it out there for people that might be interested in it … –
although I’m pretty sure that “modules of noncommutative Hopf algebras, or something like that” could turn out to be useful. However, I know much more about the latter than the former 😉
Jokes aside, I think it’s cool when mathematicians try their hand at linguistics.
In the blogs, some linguist asked for a good introduction to understand that stuff, getting the following link:
I only had the time to skim the paper, so just a few thoughts:
Lambek’s types seem to be a funny mix of semantic types and the syntactic head parameter: for one, `works’ in his example specifies what kind of input it wants, and what it outputs, i.e. in modern semantic parlour type <e,t>. `poor’ modifying `John’ says that it takes a noun, and outputs a noun. While this is achieved by predicate modification in formal semantics and not by functional application (i.e. taking an argument and outputting something), this n/n notation remarks that after the composition the part of speech type is not changed which means that `poor John’ is still more a noun, comparable to just `John’ than it is an adjective.
This is the core idea what it means to be a head in a phrase.