1 yoad winter – technion/utrecht (joint work with sela mador-haim – technion/upenn) spatial...
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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 effects
with:
- 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 X
and 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 X
and 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 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 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.