9

Indefinite Noun Phrases within the Scope of Universals

10a	Three boys[i] each bought a pizza[j].
10b	They[i] ate them[j] in the park.

Initial translation of 10a:

  ∃ B : |B| = 3 & {x | Boy(x)} ⊇ B
      ∀ b : b ∈ B .
          ∃ p : Pizza(p) . Buy(b, p)

Discourse entities from 10a:

   B1: |B1| = 3 & {x | Boy(x)} ⊇ B1
   P1: P1 = {x | Pizza(x) & ∃ y ∈ B1 . x = sk4(y)}

Semantic content:

   ∀ b : b ∈ B1. sk4(b) ∈ P1 & Buy1(b, sk4(b))

This is related to the ambiguity issue we considered with the sentence Every man loves a woman in the section on logical form.