Formal Approaches to Semantic Microvariation: Adverbial ...

in this way to account for another semantic pattern observed with anti-additive quantifiers.
As noticed by Muller (1991) and Ladusaw (1992), sentences with anti-additive
quantifiers in French allow negative concord (NC) readings. In the vast majority of
contexts, French sentences with multiple N-words are interpreted as having a single
negation. For example, although (6) contains two negative quantifiers, personne and
rien, on the most salient reading of this sentence, the two negations do not cancel each
other out.
(6) Personne a rien fait
No one has nothing done
‘No one did anything’
There is a second way of interpreting (6), namely one in which personne and rien do
cancel each other out. This is the double negation reading (‘No one did nothing’).
de Swart & Sag (2002) propose that ambiguity between double negation readings and
negative concord readings in sentences such as in (6) is due to the existence of rule of
semantic composition in the grammar of French called Resumption. This rule applies
to sequences of anti-additive quantifiers and absorbs them into a complex with a single
polyadic negative quantifier NO’. The rule for k-ary resumption is given in (7).
(7) k-ary resumption:
The k-ary resumption of a (type < 1,1 > quantifier Q is a type < 1 k ,k > quantifier
Q ′ with the following interpretation:
Q ′A 1,A 2 ,...A k
E
(R) = Q A 1×A 2 ×A k
(R)
E k
Where A 1 ...A k are subsets of the universe of discourse E.
(de Swart & Sag (2002: 385))
Crucially here, de Swart & Sag analyze (almost) all anti-additive quantifiers as being
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