I am doing a semantic derivation of the following sentence:
Cathy and Fred drank three coffees.
I know the types of each individual component but when trying to work towards t, I find a type mismatch.
I believe quantifier raising is the option that I should undertake by raising the DP 'three coffees' to a TP position and leaving a trace behind where the original is. However I am struggling with working out the layout of the rest of the sentence.
I have recently come across lambda extraction but don't know whether it is necessary to perform this in order to get a complete derivation of the sentence.
For clarification, I have the D two as being of type ((et),((et),t)) and the whole DP expression ((et),t).
Unless I have made an error with the types of the components, I am unsure how to proceed.