Transcript Slide 1

Spatial Meaning and
Quantification
Yoad Winter – Technion/Utrecht
(Joint work with Sela Mador-Haim – Technion/UPenn)
April 8, 2008 – Frankfurt
SALT paper downloadable at: www.cs.technion.ac.il/~winter
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Introduction (1): singular indefinites
We're close to a gas station.
""
2km
We're far from a gas station.
252km
68km
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137km
""
Introduction (2): plural definites
The circle is inside the rectangles.
""
The circle is outside the rectangles.
""
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Introduction (3): singular definites
The Bronx borders on the industrial zone.
""
(part of the zone)
The Bronx contains the industrial zone.
""
(the whole zone)
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Introduction (4): bare plurals
The house is close to lakes.
""
The house is far from lakes.
""

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
Empirical conclusion
The identity of the spatial preposition
affects (pseudo)-quantificational effects
with:
- Singular indfinites
- Bare plurals
- Singular and plural definites
Which mechanisms govern this behavior?
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Mechanism 1:
Spatial Meaning of Preposition
[[ outside(the lake) ]] =
area outside the eigenspace of the lake
eigenspace of the lake
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outside the lake
Mechanism 1:
Spatial Meaning of Preposition
The circle is inside
the rectangles
inside the rectangles = eigenspace of the rectangles
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Mechanism 1:
Spatial Meaning of Preposition
The circle is outside
the rectangles
outside the rectangles
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Mechanism 2:
Semantic Incorporation
[[ outside(a lake) ]] =
area outside the eigenspace of the
property for a lake
eigenspace of “a lake”
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outside a lake
Concentrating on singular indefinites:
(1) The house is close to a lake
/less than 20km from a lake

There exists a lake X such that the
house is close to X
(2) The house is far from a lake
/more than 20km from a lake

For every lake X the house is far
from X
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Questions

Which prepositions display non-existential
effects with singular indefinites?
 Locative
and temporal
 Not 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
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arguments of other predicates.
More non-existential effects
(3) The bird is more than 20m above a cloud
For every cloud X that is below the
bird, X should be more than 20m from
the bird
Don’t care …
 Not truly
universal
20m
20m
20m
20m
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More effects (cont.)
(4) The dog is less than 5m outside a doghouse
There is a doghouse X such that the
dog is less than 5m from X
and for every doghouse Y the dog is
outside Y
Hence it is not truly
existential
5m
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More effects (cont.)
(5) The house is (exactly) 100m from a lake
There is a lake X such that the house
is exactly 100m from X
and for every lake Y the house is at
least 100m from Y
100m
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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)
eigenspace function: entities to regions
[ P NPe ]et  loc-1(P(loc(Ce)))
entity
regions to
sets of entities
Example:
 outside
spatial function:
regions to regions
outside(loc(the lake))
the lake
loc-1(outside(loc(the lake)))
loc(the lake)
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Semantic incorporation of PPs

Entity denoting (Zwarts and Winter): loc-1(P(loc(Ce)))
 The
house is far from some lake
 The bird is more than 50 above every cloud

Predicative: loc-1(P(loc'(Cet)))
 The
house is far from a lake
 The airplane is more than 20m from mountains

loc'(Cet) = xCloc(x)
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Incorporation of PPs (cont.)

Example: outside a lake
a lake = {a,b,c}
loc-1(outside(loc’(a lake)))
outside(loc’(a
loc’(a lake) lake))
b
a
c
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Quantificational variability

The 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
B
quantification?
Only upward monotone Ps!
A
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 interpretation
Examples: outside, far from
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x
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
Existential
(7) This shelter was built more than 2 years after a war
Semi-universal: similar to more than 2 meters above a cloud

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)
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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 existentialuniversal 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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References
McNally, 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.
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