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

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

2. 2km 252km 68km 137km Introduction (1): singular indefinites We're close to a gas station. We're far from a gas station.

3. Introduction (2): plural definites The circle is inside the rectangles. The circle is outside the rectangles.

4. Introduction (3): singular definites The Bronx borders on the industrial zone. (part of the zone) The Bronx contains the industrial zone. (the whole zone)

5. Introduction (4): bare plurals The house is close to lakes. The house is far from lakes.

6. 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?

7. Mechanism 1: Spatial Meaning of Preposition [[ outside(the lake) ]] = area outside the eigenspace of the lake eigenspace of the lake outsidethe lake

8. Mechanism 1: Spatial Meaning of Preposition The circle is inside the rectangles insidethe rectangles = eigenspace of the rectangles

9. Mechanism 1: Spatial Meaning of Preposition The circle is outside the rectangles outsidethe rectangles

10. Mechanism 2: Semantic Incorporation [[ outside(a lake) ]] = area outside the eigenspace of the property for a lake eigenspace of “a lake” outsidea lake

11. (1) The house is close to a lake /less than 20km from a lake (2) The house is far from a lake /more than 20km from a lake 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

12. 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 arguments of other predicates.

13. 20m 20m 20m 20m 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

14. 5m 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 Hence it is not truly existential and for every doghouse Y the dog is outside Y

15. 100m 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

16. Conclusion from examples • There is a broad spectrum of quantificational effects that are sensitive to the prepositional structure in use • The house is close to a lake(existential) • The house is far from a lake(universal) • The bird is more than 20m above a cloud(semi-universal) • The dog is less than 5m outside a doghouse(semi-existential) • 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. outside(loc(the lake)) loc(the lake) Eigenspace semantics (Zwarts & Winter 2000) eigenspace function: entities to regions Example: • outside the lake loc-1(P(loc(Ce))) [ P NPe ]et entity spatial function: regions to regions regions to sets of entities loc-1(outside(loc(the lake)))

20. Semantic incorporation of PPs • Entity denoting(Zwarts and Winter): • The house is far from some lake • The bird is more than 50 above every cloud loc-1(P(loc(Ce))) • Predicative: • The house is far from a lake • The airplane is more than 20m from mountains • loc'(Cet) = xCloc(x) loc-1(P(loc'(Cet)))

21. loc-1(outside(loc’(a lake))) outside(loc’(a lake)) loc’(a lake) Incorporation of PPs (cont.) • Example: outside a lake a lake = {a,b,c} b c a

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. B A x 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 interpretation • Examples: outside, far from

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 • Prepositionmonotonicity 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. 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.