Formal Approaches to Semantic Microvariation: Adverbial ...

following definitions for beaucoup and peu.
(12) a. Let s 1 ∈ N,
For all P,Q ∈ PE, BCP
s 1
(P)(Q) = 1 iff | P ∩ Q |> s 1
b. Let s 2 ∈ N,
For all P,Q ∈ P(E), PEU
s 2
(P)(Q) = 1 iff | P ∩ Q |< s 2
where s 1 ,s 2 are contextually given standards for the cardinality of P ∩ Q.
In this paper, I will only provide explicit semantic analyses of the behaviour of peu
and beaucoup. However, my analysis of beaucoup is straightforwardly applicable to
other quantifiers that mean ‘a lot’ like énormément, pas mal, and full. Likewise, the
semantics of pas benben and pas ’yab could be assimilated to my proposal for peu
without too much trouble. I will not, however, consider in detail the behaviour of degree
quantifiers with consecutive clauses: comparatives (plus and moins) and gradation
constructions (tellement, trop and assez). The primary reason for this is that there is
not yet a clear consensus in the literature on the contribution of the consecutive clause
in specifying the ‘standard’ to which the cardinality of the de phrase complement of
these quantifiers is compared (cf. von Stechow (1984); Heim (2000); Meier (2003),
and Hacquard (2006) for different analyses of the for/pour clause with too/trop). Additionally,
the literature on comparatives is almost exclusively focused on their uses
with adjectives: where they quantify over degrees. The use of more in the nominal
domain is usually treated as a secondary use derived by type-shifting the denotation of
the noun into a set of degrees. In this paper, we are interested in what happens when
adverbs (event quantifiers) seem to be quantifying over objects; therefore, theories that
focus only on the uses of these quantifiers in the ‘degree’ domain are not so relevant
here.
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