In most frameworks you quickly get familiar with notation like PP (prepositional phrase), NP (noun phrase), VT (transitive verb), ADJ (adjective) and so forth. Categorial grammar however, bristles with things like (S\NP)\((S\NP)/(S[adj]\NP)). What’s going on here?
Aside: hopefully these are the last examples I give in English.
“Mary loves pizza”. “Mary” is a singular personal name, “pizza” is a mass noun, and those are both sorts of NP. What about “loves”? It’s (S\NP)/NP. A simpler example is “Ice melts”. “Ice” is an NP, and “melts” here is S\NP. The backslash in Y\X means “give me something of type X to my left and I’ll give you a Y“.
So (S\NP)/NP, with a forward slash and a backslash, takes NPs to the left and right, and gives you an S, or a sentence.
In principle Gaelic verbs should have type (S/NP)/NP, but I have never seen a sentence exactly like this. “Mary loves pizza”, after all, is only OK because “loves” is stative. Unless you do the marketing for McDonald’s.