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Yoad Winter – Technion/Utrecht(Joint work with Sela Mador-Haim – Technion/UPenn)

Spatial Meaning and Quantification

SALT paper downloadable at: www.cs.technion.ac.il/~winter

April 8, 2008 – Frankfurt

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""

252km

137km

68km

""We're far from a gas station.

2km

We're close to a gas station.

Introduction (1): singular indefinites

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""

""The circle is outside the rectangles.

The circle is inside the rectangles.

Introduction (2): plural definites

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""""

The Bronx borders on the industrial zone.

The Bronx contains the industrial zone.

(part of the zone)

(the whole zone)

Introduction (3): singular definites

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""""The house is far from lakes.

The house is close to lakes.

Introduction (4): bare plurals

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The identity of the spatial preposition affects (pseudo)-quantificational effectswith:

- Singular indfinites- Bare plurals- Singular and plural definites

Empirical conclusion

Which mechanisms govern this behavior?

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[[ outside(the lake) ]] = area outside the eigenspace of the lake

Mechanism 1: Spatial Meaning of Preposition

eigenspace of the lake outside the lake

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inside the rectangles = eigenspace of the rectangles

insideThe circle is the rectangles

Mechanism 1: Spatial Meaning of Preposition

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outside the rectangles

outsideThe circle is the rectangles

Mechanism 1: Spatial Meaning of Preposition

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eigenspace of “a lake” outside a lake

[[ outside(a lake) ]] = area outside the eigenspace of the

property for a lake

Mechanism 2: Semantic Incorporation

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Concentrating on singular indefinites:

There exists a lake X such that the house is close to X

For every lake X the house is far from X

The house is close to a lake/less than 20km from a lake

)1( The house is far from a lake/more than 20km from a lake

)2(

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Questions Which prepositions display non-existential

effects with singular indefinites?Locative and temporalNot upward monotone

Which singular indefinites?Predicative indefinites (a vs. some)

What’s “Semantic Incorporation”?Zimmermann, McNally, Van Geenhoven, and

others: a mechanism that allows predicative (property denoting) indefinites to become arguments of other predicates.

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More non-existential effects(3) The bird is more than 20m above a cloud

20m

20m

20m

20m

For every cloud X that is below the bird, X should be more than 20m from the bird

Don’t care… Not truly universal

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More effects (cont.)(4) The dog is less than 5m outside a doghouse

5m

There is a doghouse X such that the dog is less than 5m from Xand for every doghouse Y the dog is outside Y

Hence it is not truly existential

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More effects (cont.)(5) The house is (exactly) 100m from a lake

100m

There is a lake X such that the house is exactly 100m from Xand for every lake Y the house is at least 100m from Y

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Conclusion from examples There is a broad spectrum of quantificational effects that

are sensitive to the prepositional structure in use(1) The house is close to a lake (existential)

(2) The house is far from a lake (universal)

(3) The bird is more than 20m above a cloud (semi-universal)

(4) The dog is less than 5m outside a doghouse (semi-existential)

(5) The house is (exactly) 100m from a lake (combination) What kind of mechanism can account for the different

quantificational effects in (1)-(5)?

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Proposed solution

A predicative denotation of the indefinite A building: x. building(x)

Locatives take such predicates as arguments semantic incorporation

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Semantic incorporation Motivation: narrow scope of indefinites Obligatory narrow scope:

There sentences (McNally 1992,1998): There isn't a cloud in the sky

Transitive constructions in West-Greenlandic (Van Geenhoven 1998):

John fish-buy-NEG-IND-[tr]-3sg ( / *) Optional narrow scope as opposed to other NPs

(Zimmermann 1993, Van Geenhoven and McNally 2005) John is looking for a dog/every dog

Claim: Also in PPs, non-existential indefinites appear due to narrow scope via incorporation

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Eigenspace semantics (Zwarts & Winter 2000)

Example:outside the lake

loc(the lake)

outside(loc(the lake))

loc-1(outside(loc(the lake)))

loc-1(P(loc(Ce)))

entity

eigenspace function: entities to regions

spatial function :regions to regionsregions to

sets of entities

[ P NPe ]et

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Semantic incorporation of PPs

loc-1(P(loc(Ce)))

Predicative: The house is far from a lakeThe airplane is more than 20m from mountains

loc'(Cet) = xCloc(x)

Entity denoting (Zwarts and Winter):The house is far from some lakeThe bird is more than 50 above every cloud

loc-1(P(loc'(Cet)))

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Incorporation of PPs (cont.)

Example: outside a lake

a lake = {a,b,c}

a

b

c

loc’(a lake)outside(loc’(a lake))

loc-1(outside(loc’(a lake)))

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Quantificational variabilityThe house is close to a lake

The house is close to a lake iff it is close to the union of the eigenspaces of all lakes

It is sufficient that the house is close to some point in some lake (existential)

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Quantificiational variability (cont.)

The house is far from a lake The house is far from a lake iff it is far from the

union of the eigenspaces of all lakes The house needs to be far from all points in the lakes

(universal)

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Quantificiational variability (cont.)The house is exactly 100m from a lake Measure phrases in Zwarts and Winter (2000) take

distance from the closest point. This entails that there is a point in the union of the lakes which is 100m from the house, and that it is among the closest points to the house.

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Quantificiational variability (cont.)

The dog is less than 5m outside a doghouse Less than 5m from the union of the eigenspaces of

the doghouses, and not in that area

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Point monotonicity (Zwarts and Winter)

Which prepositions support existential quantification?

Only upward monotone Ps!P is upward monotone if for all eigenspaces

A,B s.t. A B: x P A x P B.Examples: inside, close to

Similarly, only prepositions that are downward monotone lead to universal interpretationExamples: outside, far from

B

A

x

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Downward Monotonicity – standard tests Downward/Upward entailing environments:

The house is far from a lake The house is far from a small lake

The house is close to a lake The house is close to a small lake

NPI licensing(6) The house is far from/*close to any

lake

Not accounted for if PPs take entity arguments!

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Other PPs Analogous effects with temporal PPs:

(6) This shelter was built less than 2 years after a war

(7) This shelter was built more than 2 years after a war

NPI licensing: before/*after any war Conclusion: temporal PPs can likewise incorporate

their complement Directional PPs do not incorporate (thanks to J.

Zwarts):(8) We went around a lake - (existential only)

Existential

Semi-universal: similar to more than 2 meters above a cloud

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Summary and conclusions Prepositions with indefinite complements exhibit a

wide spectrum of quantificational variability A result of incorporation between predicative

indefinites and prepositions Preposition monotonicity governs existential-

universal variability Monotonicity is also verified by standard tests (NPI

licensing, entailment) Incorporation – a general process with both locative

and temporal prepositions

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ReferencesMcNally, L. 1992. An Interpretation for the English Existential Construction. Ph.D. Diss., UCSC. Published 1997. Garland, New York

McNally, L. 1998. Existential sentences without existential quantification. Linguistics and Philosophy 21, 353-392

McNally, L. and V. Van Geenhoven 2005. On the property analysis of opaque complements. Lingua 115, 885-914.

Van Geenhoven, V. 1998. Semantic Incorporation and Indefinite Descriptions. CSLI Publications.

Zimmermann, T.E. 1993. On the proper treatment of opacity in certain verbs. Natural Language Semantics 1, 149-179.

Zwarts, J. and Y. Winter 2000. Vector space semantics. Journal of Logic, Language and Information, 171-213.