Most words in categorial grammar are functions. In English, a transitive verb such as “eats” is a function that takes two NP arguments and gives you a clause, S, back. The notation for this is (S/NP)\NP. (Aside: This is rather like defining a function in a programming language, except that void isn’t a type.)
What does this functional approach tell us about particles like a and chan? To answer this I’ll need to set out the different sort of clauses I’ve seen in Scottish Gaelic. The notation here is based on CCGbank, which itself is based on that of the Penn Treebank, and I’ve marked new ones as such.
- S[adj]: predicative adjective. Example: snog in Tha i snog.
- S[dcl]: ordinary declarative sentence. Tha i snog.
- S[q]: polar question. A bheil i snog?
- (new) S[neg]: negative question. Chan eil i snog.
- (new) S[negq]: negative polar question. Nach eil i snog?
- S[wh]: wh-question: Ciamar a tha thu?
- (new) S[n]: verbal noun-headed small clause. iarraidh cofaidh in Tha mi ag iarraidh cofaidh.
- S[em]: embedded declarative. a tha thu in Ciamar a tha thu?
- (new) S[dep]: dependent verb-headed clause. bheil i snog in A bheil i snog?
- (new) S[a]: a-infinitive. a bhith a’ dannsadh
The five new ones need some explanation. S[neg] and S[negq] are motivated by the clear fourfold division of ordinary sentences into positive, interrogative, negative and interrogative negative. S[n], relating as it does to a verbal noun, replaces S[ed], S[pss] and S[ng] in the CCGbank scheme for English. S[a] is somewhat like S[to] in the CCGbank scheme but not exactly the same as it contains a verbal noun somewhere, and lastly S[dep] presents a phenomenon we simply don’t get in English.
So what do particles do here? Let’s take a few examples from last week’s An Litir Bheag:
Here cha is a function mapping a dependent clause to a negative sentence.
There is a lot going on there. I’ve thought of adverbs as taking a sentence in and giving you a sentence back. Hence gu when it serves to make an adverb out of an adjective, takes S[adj] as its argument and gives you a function that takes a S[dcl] and gives you back S[dcl]. na, as in “that which”, is a function that takes a S[dcl] and gives you a NP back. I’m using shorthands for conjunctions and PPs, but these are both described in the literature.
Potential point for discussion: I’ve treated ag, a’, air, gu and ri when they introduce verbal nouns as PP/S[n]. But maybe they should be a clause type of their own. Needs more thought.