e.g. ⟦blond boy⟧M = [λx∈De. 1 iff ⟦blond⟧M(x)=1 and ⟦boy⟧M(x)=1]
Need the semantics of: ti, C, and whoi
⟦α⟧a,M = the denotation of α with respect to model M and assignment function a
⟦t2⟧a,M = a(2) = John ⟦t5⟧a,M = a(5) = Daniel
⟦t2⟧b,M = b(2) = John ⟦t5⟧b,M = b(5) = Hanna
⟦John⟧a,M = ⟦John⟧b,M ⟦man⟧a,M = ⟦man⟧b,M = [λx∈De. 1 iff x is a man in M] ⟦Mary likes London⟧a,M = ⟦Mary likes London⟧b,M
Since C' is of type t, the relative pronoun needs to turn it into a type-⟨e,t⟩ function.
At the same time we want to account for the dependency between who and t.
NB: a[3→Paris] doesn't mean 'a maps 3 to Paris'. a[3→Paris] means 'a[3→Paris] maps 3 to Paris and for all other indices, it's just like a'. And typically, a ≠ a[3→Paris]. --- # Exercise: Assignment Modification What are the following modified assignments? 1. g[1→Ken] 2. g[2→George] 3. g[1→George][2→Eva] 4. g[3→George][3→Eva] --- Now we have: > ⟦who3 C t3 is blond⟧a,M = [λx∈De. 1 iff x is blond in M] ⟦who3 C t3 is blond⟧a,M = [λx∈De. ⟦C t3 is blond⟧a[3→x],M] (PA) = [λx∈De. ⟦C⟧a[3→x],M(⟦t3 is blond⟧a[3→x],M)] (FA) = [λx∈De. \[λv∈Dt. v](⟦t3 is blond⟧a[3→x],M)] (Lexicon) = [λx∈De. ⟦t3 is blond⟧a[3→x],M] (λ-conv.) = [λx∈De. ⟦is blond⟧a[3→x],M(⟦t3⟧a[3→x],M)] (FA) = [λx∈De. ⟦is blond⟧a[3→x],M(a\[3→x](3))] (TR) = [λx∈De. ⟦is blond⟧a[3→x],M(x)] = [λx∈De. ⟦is⟧a[3→x],M(⟦blond⟧a[3→x],M)(x)] (FA) = ... = [λx∈De. ⟦blond⟧a[3→x],M(x)] (FA) = ... = [λx∈De. 1 iff x is blond in M] (= ⟦blond⟧a,M) --- # Summary
NB: (3) is not possible with subject relatives. We assume that this is a morpho-syntactic constraint. (3') *a man (RP5) (C) t5 is blond