Formal Approaches to Semantic Microvariation: Adverbial ...

We must now make some modification to de Swart & Sag’s Resumption rule to
accommodate these complex predicates: Resumption takes a string of k anti-additive
GQs, and creates quantifier of type < 1 k ,k >, where k matches the number of common
noun denotations that are arguments of the quantifier NO. The way this rule is currently
defined, after NO ′ is combined with a sequence of properties, the resulting quantifier
has a domain that is limited to relations of the arity of the number of N-words that have
been absorbed. Since Restrict’ is a non-saturating operation, NO ′A 1...A k will need to be
applied to a k + 1-ary relation. For example, application of Resumption in (12) yields
(13).
(13) NO ′HUMAN,HUMAN (GIVE DE(BOOK))
Disregarding the event argument, NO ′ first combines with 2 properties, so, by Resumption,
NO ′HUMAN,HUMAN is of type < 2 >. However, GIV E DE(BOOK) is a ternary
relation. Furthermore, if we assume, as I have been doing, that verbs contain an event
argument, all predicates will be at least k+1 relations, for k the number of anti-additive
quantifiers in the sentence. I therefore propose that Resumption maps sequences of
unary relations to a function whose domain includes all the n-ary relations, for finite
n. This function is defined in (14).
(14) For all R ∈ ⋃ n∈N P(E n ), NO ′A 1...A k (R) = 1 iff R =Ø.
The revision of Resumption would map sequences of one-place predicates to a very
general quantifier, one that takes a relation of any arity, and maps it to 0 if it is not
the null relation. Of course this rule now looks a lot less like a “resumption” in the
traditional sense (Keenan & Westerstahl (1997); Peters & Westerstahl (2006)) 3 . To
3 And indeed, as de Swart & Sag note, their Resumption rule also differs from the definition presented
in Keenan & Westerstahl (1997).
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