Formal Approaches to Semantic Microvariation: Adverbial ...

(12) For all P ∈ P(E),∃(P) = 1 iff P ≠ Ø
(12) can be extended to binary relations in a number of ways. Firstly, we can extend
it in the same way in which we extended BCP 1 to BCP GQ , namely, we can take the
accusative extension.
(13) Accusative Extension (Keenan (1987: 3)):
For F basic, F ACC or the accusative case extension of F is that extension of
F which sends each binary relation R to {b : F(bR) = 1}. (bR = de f {a :<
b,a >∈ R})
The function given as BCP GQ in the previous chapter is simply a generalization of (13)
to n-ary relations. So the accusative extension of ∃ is (14).
(14) For all R ∈ P(E × E), ∃ ACC (R) = {b : bR ≠ Ø}
However, there is another obvious way in which we can extend ∃; that is, instead of
looking at what ∃ does to the second co-ordinate of a relation, we can look at what it
does to the first co-ordinte. This is the nominative extension of ∃.
(15) Nominative Extension (Keenan (1987: 4)):
For F basic, F NOM or the nominative case extension of F is that extension
of F which sends each binary relation R to {b : F(Rb) = 1}. (Rb = de f {a :<
a,b >∈ R})
I now show that BCP QF is equivalent to the case where beaucoup ‘out-scopes’ the
existential quantifier. In other words, I show that BCP QF is the same function as BCP 1 ◦
∃ NOM . This is stated as Theorem 2 in (16).
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