First up, “to be”.
Bi has three forms in the present tense, according to whether it’s positive, interrogative, negative or negative interrogative, all thanks to particles which I don’t know whether they’re a VMOD or a P or a what.
- Positive: Tha mi sgìth (I am tired). Tha is independent so is (S/NP)/ADJ.
- Negative: Chan eil mi sgìth (I am not tired). Eil is dependent, so its type will be ((S\VMOD)/NP)/ADJ.
- Negative interrogative: Nach eil thu sgìth? (Are you not tired?) Same as above.
- Interrogative: A bheil thu sgìth? (Are you tired?) Bheil is dependent again but whereas most verbs just have a dependent and an independent form in any one tense, bi has two dependent forms. So, what to do?
Whatever happens, we have a tree at the top which says something like (Vspec Vbar). I don’t especially like this because eil thu sgìth, the Vbar, isn’t a constituent. I’m willing to lay money that there are no song titles that begin “Eil”. A coordination test for constituency, incidentally, isn’t decisive in English because one thing that categorial grammar is good at is non-constituent coordination, say in “Mary loves pizza and Tim rice”.
So either we commit ourselves to a type S/Vbar for a or chan or nach, which is potentially good because you could parse the entire sentence with forward composition, of which more tomorrow, or to assign eil type ((S\Vspec_neg)/NP)/ADJ and bheil type ((S\Vspec_int)/NP/ADJ. More types will be needed for all of these forms, because bi isn’t just for adjectives!
Tomorrow: what is the simplest parser that could possibly work?