1 Yoad Winter – Technion/Utrecht (Joint work with Sela Mador-Haim – Technion/UPenn) Spatial...
-
Upload
santiago-brainard -
Category
Documents
-
view
214 -
download
0
Transcript of 1 Yoad Winter – Technion/Utrecht (Joint work with Sela Mador-Haim – Technion/UPenn) Spatial...
1
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
2
""
252km
137km
68km
""We're far from a gas station.
2km
We're close to a gas station.
Introduction (1): singular indefinites
3
""
""The circle is outside the rectangles.
The circle is inside the rectangles.
Introduction (2): plural definites
4
""""
The Bronx borders on the industrial zone.
The Bronx contains the industrial zone.
(part of the zone)
(the whole zone)
Introduction (3): singular definites
5
""""The house is far from lakes.
The house is close to lakes.
Introduction (4): bare plurals
6
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?
7
[[ outside(the lake) ]] =
area outside the eigenspace of the lake
Mechanism 1: Spatial Meaning of Preposition
eigenspace of the lake outside the lake
8
inside the rectangles = eigenspace of the rectangles
insideThe circle is the rectangles
Mechanism 1: Spatial Meaning of Preposition
9
outside the rectangles
outsideThe circle is the rectangles
Mechanism 1: Spatial Meaning of Preposition
10
eigenspace of “a lake” outside a lake
[[ outside(a lake) ]] =
area outside the eigenspace of the property for a lake
Mechanism 2: Semantic Incorporation
11
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(
12
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.
13
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
14
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
15
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
16
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)?
17
Proposed solution
A predicative denotation of the indefinite A building: x. building(x)
Locatives take such predicates as arguments semantic incorporation
18
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
19
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
20
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)))
21
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)))
22
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)
23
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)
24
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.
25
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
26
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
27
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!
28
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
29
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
30
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.