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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

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

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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

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

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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?

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

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8 inside the rectangles = eigenspace of the rectangles insideThe circle isthe rectangles Mechanism 1: Spatial Meaning of Preposition

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9 outside the rectangles outsideThe circle isthe rectangles Mechanism 1: Spatial Meaning of Preposition

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

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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)

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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) Whats 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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13 More non-existential effects (3) The bird is more than 20m above a cloud 20m For every cloud X that is below the bird, X should be more than 20m from the bird Dont care … Not truly universal

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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

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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

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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)?

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17 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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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

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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(C e ))) entity eigenspace function: entities to regions spatial function: regions to regions regions to sets of entities [ P NP e ] et

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20 Semantic incorporation of PPs loc -1 (P(loc(C e ))) Predicative: The house is far from a lake The airplane is more than 20m from mountains loc'(C et ) = x C loc(x) 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'(C et )))

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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)))

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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)

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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)

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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.

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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

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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 interpretation Examples: outside, far from B A x

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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!

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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

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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

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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.

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