The Salish language Stat'imc'ets does not allow quantifiers within the scope of other quantifiers. There is only a cumulative reading in such cases, i.e. "every boy saw 5 birds" is true if every boy saw a bird and the total number of birds seen was 5. This can be modeled in frame semantics, in semantic dependency graphs (SDG, the semantic representation language used in the talk) or in certain versions of event semantics by a projection semantics: the projection of the reported events by the thematic role experiencer gives all the boys and its projection by the thematic role theme the 5 observed birds. Cumulative readings, also claimed to be the default readings in many cases for English sentences with two NPs, are simple in such frameworks and complex in semantic representation formalisms based on Mostowski's generalised quantifiers., like Montague grammar or DRT -which can be seen as an argument in favour of the first and against the latter style of semantic representation.

 

Stat'imc'ets has however a separate morphological class of dependent NPs (ku+noun) that must be licensed by other quantifiers.

These behave as NPs in the scope of their licensing quantifier and reconstructing that meaning in SDG in the standard way is complex and unintuitive.

It is however possible to interpret the dependent NPs directly as functions that map the denotation of their licensing NP to normal NP values.

This preserves the projection properties of the licensing NP and turns out to be just as feasible for English, in which any NP can be in the scope of another quantifier. Possessive NPs are a plausibkle source for the reanalysis that makes them into dependent NPs and thus for a historical account of the possibility orf one NP being in the scope of another.

 

The resulting approach makes a number of things remarkably easy.

 

1. It gives a markedness order over the different readings of NP V NP sentences in which overt marking and absurdity pushes the interpreter to the least marked

interpretation of the sentence, instead of the 64 readings standardly assumed in the worst case.

 

2. The mixed cumulative quantificational cases noted by Barry Schein fall out of the process described in 1.

 

3. The dependent anaphora that motivated Martin van den Berg's dissertation get a trivial analysis.

 

4. Branching quantifiers likewise fall out of the process given in 1.

 

5. The disharmony in the head noted by Zwicky disappears (there is no longer something that can be called the semantic head)

 

6. Free choice items can be interpreted simply and naturally

 

7. In recent work, Viola Schmitt has shown that all conjunction gives rise to cumulative readings -and consequently that a Boolean approach

is just wrong for natural language conjunction. Boolean behaviour can however be restored by making the conjunction dependent on other conjunctions

and the same markers (each, both) that force dependency between NPs are used.

 

8. Dependency also seems the right way for an analysis of negative polarity items. But this is work for the future.

 

As indicated, the analysis of quantification proposed has applications beyond natural language. The paper shows that in natural language semantics, it has a strong typological and semantic underpinning. The notion of projection as a semantic operation is still central and as such also the proposed analysis of quantification makes a strong case for frame semantics, SDG or (certain kinds of) event semantics.