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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.

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    Where is the mismatch? What are the types you assigned to the individual components, and at which point with which types does the computation fail?
    – lemontree
    Apr 9 '19 at 13:25
  • Cathy Fred type (e)
    – Lyhbm
    Apr 9 '19 at 14:46
  • drank and coffees (et)
    – Lyhbm
    Apr 9 '19 at 14:47
  • and (e(e,e), three (et)(et)t))
    – Lyhbm
    Apr 9 '19 at 14:48
  • The mismatch occurs at the VP with the V 'drank' and DP 'three coffees'
    – Lyhbm
    Apr 9 '19 at 14:49
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As a little intellectual exercise, I looked around a little and found an online PDF using your notation - "Elements of Formal Semantics" (http://www.phil.uu.nl/~yoad/efs/EFS-ch3-online.pdf).

According to page 89, "drank" is of type e(et), not et, as it's transitive. The "and" would be t(tt), not e(ee) according to that page, but that may be an omission.

My reputation is not yet enough to comment, so I wrote it here, though it's not a complete answer - more an idea how to go forward. Hope it helps anyway!

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    Thank you for correcting the transitive verb. Through experimenting with different constitutents I found that and could also be of type (et)(et)(et) and e(ee) if ‘and’ conjoined verb phrases or determiner phrases. When I attempt the derivation with t(tt), there is still a type mismatch. So I am stuck with regards to raising the quantified DP.
    – Lyhbm
    Apr 9 '19 at 23:05

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