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Split-scope definites How the can mean two things at once Dylan - - PowerPoint PPT Presentation

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Split-scope definites How the can mean two things at once Dylan Bumford 18 February 2016 New York University Definite description Wisdom: the NP refers to the single salient NP in the context the hat = x , where x is

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SLIDE 1

Split-scope definites

How ‘the’ can mean two things at once

Dylan Bumford 18 February 2016

New York University

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SLIDE 2

Definite description

Wisdom: ‘the NP’ refers to the single salient ‘NP’ in the context the hat = x, where x is the unique relevant hat Proposal: Definite determination split into two subprocesses. the hat = one (· · · (some hat)) When things intervene, ‘the hat’ may end up one among many Payoffs:

  • Haddock readings
  • Relative superlatives
  • Possibly other strange readings of quantificational adjectives
  • Emerging uniformity in the theory of cardinal modification

1/17

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SLIDE 3

Definite description

Wisdom: ‘the NP’ refers to the single salient ‘NP’ in the context the hat = x, where x is the unique relevant hat Proposal: Definite determination split into two subprocesses. the hat = one (· · · (some hat)) When things intervene, ‘the hat’ may end up one among many Payoffs:

  • Haddock readings
  • Relative superlatives
  • Possibly other strange readings of quantificational adjectives
  • Emerging uniformity in the theory of cardinal modification

1/17

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SLIDE 4

Definite description

Wisdom: ‘the NP’ refers to the single salient ‘NP’ in the context the hat = x, where x is the unique relevant hat Proposal: Definite determination split into two subprocesses. the hat = one (· · · (some hat)) When things intervene, ‘the hat’ may end up one among many Payoffs:

  • Haddock readings
  • Relative superlatives
  • Possibly other strange readings of quantificational adjectives
  • Emerging uniformity in the theory of cardinal modification

1/17

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SLIDE 5

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

(2) [Horacek 1995] the table with the apple and the banana Nothing especially salient about the relevant fruit

2/17

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SLIDE 6

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

(2) [Horacek 1995] the table with the apple and the banana Nothing especially salient about the relevant fruit

2/17

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SLIDE 7

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

(2) [Horacek 1995] the table with the apple and the banana Nothing especially salient about the relevant fruit

2/17

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SLIDE 8

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

(2) [Horacek 1995] the table with the apple and the banana Nothing especially salient about the relevant fruit

2/17

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SLIDE 9

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

(2) [Horacek 1995] the table with the apple and the banana Nothing especially salient about the relevant fruit

2/17

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SLIDE 10

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

2/17

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SLIDE 11

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

Constraint Satisfaction Problem

x y rabbit x x in · · · hat y

Unique x and y satisfying these simultaneous constraints

  • Noncompositional. Worse, circular!

2/17

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SLIDE 12

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

Constraint Satisfaction Problem

x y rabbit x x in · · · hat y

Unique x and y satisfying these simultaneous constraints

  • Noncompositional. Worse, circular!

2/17

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SLIDE 13

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

Constraint Satisfaction Problem

x y rabbit x x in · · · hat y

Unique x and y satisfying these simultaneous constraints

  • Noncompositional. Worse, circular!

2/17

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SLIDE 14

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

Constraint Satisfaction Problem

x y rabbit x x in y hat y

Unique x and y satisfying these simultaneous constraints

  • Noncompositional. Worse, circular!

2/17

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SLIDE 15

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

Constraint Satisfaction Problem

x y rabbit x x in y hat y

Unique x and y satisfying these simultaneous constraints

  • Noncompositional. Worse, circular!

2/17

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SLIDE 16

Haddock descriptions

(1) [Haddock 1987] the rabbit in the hat What about H2?

  • cf. #The hat is my favorite

Constraint Satisfaction Problem

x y rabbit x x in y hat y

Unique x and y satisfying these simultaneous constraints

  • Noncompositional. Worse, circular!

2/17

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SLIDE 17

Relative superlatives

(2) [Szabolcsi 1986] the girl who got the fewest leters (3) a. *When was there the rabbit in the garden? b. When were there the most rabbits in the garden? (4) the rabbit in the biggest hat

3/17

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SLIDE 18

Relative superlatives

(2) [Szabolcsi 1986] the girl who got the fewest leters ??? ???? (3) a. *When was there the rabbit in the garden? b. When were there the most rabbits in the garden? (4) the rabbit in the biggest hat

3/17

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SLIDE 19

Relative superlatives

(2) [Szabolcsi 1986] the girl who got the fewest leters ??? ???? (3) a. *When was there the rabbit in the garden? b. When were there the most rabbits in the garden? (4) the rabbit in the biggest hat

3/17

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SLIDE 20

Relative superlatives

(2) [Szabolcsi 1986] the girl who got the fewest leters ??? ???? (3) a. *When was there the rabbit in the garden? b. When were there the most rabbits in the garden? (4) the rabbit in the biggest hat

3/17

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SLIDE 21

Relative superlatives

(2) [Szabolcsi 1986] the girl who got the fewest leters ??? ???? (3) a. *When was there the rabbit in the garden? b. When were there the most rabbits in the garden? (4) the rabbit in the biggest hat

3/17

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SLIDE 22

Relative superlatives

(2) [Szabolcsi 1986] the girl who got the fewest leters ??? ???? (3) a. *When was there the rabbit in the garden? b. When were there the most rabbits in the garden? (4) the rabbit in the biggest hat

3/17

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SLIDE 23

Relative superlatives via constraint satisfaction?

(5) the rabbit in the biggest hat

x y rabbit x x in hat y

4/17

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SLIDE 24

Relative superlatives via constraint satisfaction?

(5) the rabbit in the biggest hat

x y rabbit x x in · · · hat y

4/17

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SLIDE 25

Relative superlatives via constraint satisfaction?

(5) the rabbit in the biggest hat

x y rabbit x x in · · · hat y

4/17

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SLIDE 26

Relative superlatives via constraint satisfaction?

(5) the rabbit in the biggest hat

x y rabbit x x in · · · hat y

4/17

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SLIDE 27

Relative superlatives via constraint satisfaction?

(5) the rabbit in the biggest hat

x y rabbit x x in y hat y

4/17

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SLIDE 28

Relative superlatives via constraint satisfaction?

(5) the rabbit in the biggest hat

x y rabbit x x in y hat y

4/17

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SLIDE 29

Decomposing definiteness

The basic idea: definiteness is a two-step process        G if

  • {g ν | g ∈ G}
  • = 1

#

  • therwise

1ν {ν → x | hat x} someν hat theν

5/17

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SLIDE 30

Decomposing definiteness

The basic idea: definiteness is a two-step process        G if

  • {g ν | g ∈ G}
  • = 1

#

  • therwise

1ν {ν → x | hat x} someν hat theν

5/17

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SLIDE 31

Decomposing definiteness

The basic idea: definiteness is a two-step process        G if

  • {g ν | g ∈ G}
  • = 1

#

  • therwise

1ν {ν → x | hat x} someν hat theν Dynamic Semantics

  • Denotations are sets of assignments
  • Indefinites introduce nondeterministic referents

5/17

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SLIDE 32

Decomposing definiteness

The basic idea: definiteness is a two-step process        G if

  • {g ν | g ∈ G}
  • = 1

#

  • therwise

1ν {ν → x | hat x} someν hat theν Dynamic Semantics

  • Denotations are sets of assignments
  • Indefinites introduce nondeterministic referents

5/17

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SLIDE 33

Decomposing definiteness

The basic idea: definiteness is a two-step process        G if

  • {g ν | g ∈ G}
  • = 1

#

  • therwise

1ν {ν → x | hat x} someν hat theν Dynamic Semantics

  • Denotations are sets of assignments
  • Indefinites introduce nondeterministic referents

5/17

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SLIDE 34

Decomposing definiteness

The basic idea: definiteness is a two-step process        G if

  • {g ν | g ∈ G}
  • = 1

#

  • therwise

1ν {ν → x | hat x} someν hat theν

5/17

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SLIDE 35

Decomposing definiteness

The basic idea: definiteness is a two-step process        G if

  • {g ν | g ∈ G}
  • = 1

#

  • therwise

1ν {ν → x | hat x} someν hat theν

5/17

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SLIDE 36

Teasing the pieces apart

(6) the [rabbit in the hat] (7) the [rabbit in the biggest hat]

6/17

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SLIDE 37

Teasing the pieces apart

(6) the [rabbit in the hat] some

  • ne

some

  • ne

(7) the [rabbit in the biggest hat]

6/17

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SLIDE 38

Teasing the pieces apart

(6)

  • ne [some rabbit in [one [some hat]]]

(7) the [rabbit in the biggest hat]

6/17

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SLIDE 39

Teasing the pieces apart

(6) the [rabbit in the hat] some

  • ne

some

  • ne

(7) the [rabbit in the biggest hat]

6/17

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SLIDE 40

Teasing the pieces apart

(6)

  • ne [one [ some rabbit in some hat]]

some

  • ne

some

  • ne

(7) the [rabbit in the biggest hat]

6/17

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SLIDE 41

Teasing the pieces apart

(6)

  • ne [one [ some rabbit in some hat]]

(7) the [rabbit in the biggest hat]

6/17

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SLIDE 42

Teasing the pieces apart

(6) the [rabbit in the hat] (7) the [rabbit in the biggest hat]

6/17

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SLIDE 43

Teasing the pieces apart

(6) the [rabbit in the hat] (7) the [rabbit in the biggest hat] some

  • ne

some

  • ne biggest

6/17

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SLIDE 44

Teasing the pieces apart

(6) the [rabbit in the hat] (7)

  • ne [some rabbit in [one biggest [some hat]]]

6/17

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SLIDE 45

Teasing the pieces apart

(6) the [rabbit in the hat] (7) the [rabbit in the biggest hat] some

  • ne

some

  • ne biggest

6/17

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SLIDE 46

Teasing the pieces apart

(6) the [rabbit in the hat] (7)

  • ne [one biggest [ some rabbit in some hat]]

some

  • ne

some

  • ne biggest

6/17

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SLIDE 47

Teasing the pieces apart

(6) the [rabbit in the hat] (7)

  • ne [one biggest [ some rabbit in some hat]]

6/17

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SLIDE 48

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 49

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 50

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 51

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 52

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 53

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 54

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 55

Haddock effects: Interleaved definites

1u 1ν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu theν

7/17

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SLIDE 56

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 57

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 58

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 59

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 60

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 61

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 62

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 63

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν Superlative as filter Keep only the assignments that are undominated in their choice of ν Sν G ≔ {g ∈ G | ¬∃g′ ∈ G. g′ν > g ν}

8/17

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SLIDE 64

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 65

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 66

Relative superlatives: Delayed maximality filter

1u 1ν ◦ Sν ν → x u → y

  • hat x, rab y, in x y
  • someu

rabbit in {ν → x | hat x} someν hat theu the biggestν

8/17

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SLIDE 67

Connections and applications: Qantificational adjectives

Range of quantificational adjectives that ride on the scope of the definite article (8) [Bylinina et al. 2014] John gave Mary the first telescope a. John was the first to give Mary a telescope (9) [Coppock & Beaver 2015] Mary didn’t score the only goal a. Mary wasn’t the only one to score a goal (10) [Barker 2007] Ann read the same book yesterday and today a. Ann read a book yesterday and a book today; they where the same

9/17

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SLIDE 68

Connections and applications: Split numerosity

And more generally, cardinality-testing denotations appear happy to take delayed action (11) [Cresti 1995] You should talk to at least three professors a. You should talk to some professors; three at the least (12) [Brasoveanu 2012] Exactly three boys saw exactly five movies a. Some boys saw some movies; three and five, to be exact

10/17

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SLIDE 69

Zooming out: Multidimensionality in meaning

Plenty of constructions known to contribute two kinds of meaning at once

  • Focus

I gave the book to JOHN

  • Conventional Implicature and presupposition

John, a linguist, received a mysterious book

  • Anaphora and discourse referent management

A man walked in; he asked John about his book

  • Alternative generation

John either liked or hated his book; I can’t remember

11/17

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SLIDE 70

Scope as multidimensional meaning

  • Qantification is a kind of multidimensional effect

everyx student John talked to x

  • Definiteness is just like that, but more
  • neu

someu John talked to u

12/17

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SLIDE 71

Conclusion

  • Definiteness is semantically bipartite

1ν someν hat theν

  • Mismatches in the execution of the parts accounts for relative

readings of definites and superlatives, and possibly other quantificational adjectives

  • Encourages a multidimensional view of meaning, in which

different subprocesses of a denotation may act at different times on different arguments

13/17

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SLIDE 72

Thanks

Thanks!

14/17

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SLIDE 73

References I

Barker, Chris. 2007. Parasitic scope. Linguistics and Philosophy 30(4). 407–444. http://dx.doi.org/10.1007/s10988-007-9021-y. Brasoveanu, Adrian. 2012. Modified numerals as post-suppositions. Journal of Semantics http://dx.doi.org/10.1093/jos/ffs003. Bylinina, Lisa, Natalia Ivlieva, Alexander Podobryaev & Yasutada Sudo. 2014. A non-superlative semantics for ordinals and the syntax of comparison classes. In Proceedings of the 45th meeting of the north east linguistic society (NELS 45), . Coppock, Elizabeth & David Beaver. 2015. Definiteness and determinacy. Linguistics and Philosophy 38(5). 377–435. http://dx.doi.org/10.1007/s10988-015-9178-8. Cresti, Diana. 1995. Extraction and reconstruction. Natural Language Semantics 3(1). 79–122. Haddock, Nicholas J. 1987. Incremental interpretation and Combinatory Categorial

  • Grammar. In Proceedings of the 10th international joint conference on artificial

intelligence, vol. 2, 661–663. Morgan Kaufmann Publishers Inc. Horacek, Helmut. 1995. More on generating referring expressions. In Proceedings of the fifh European workshop on natural language generation, 43–58. Leiden, The Netherlands. Szabolcsi, Anna. 1986. Comparative superlatives. In MIT Working Papers in Linguistics 8, 245–265. Cambridge, MA: MIT. 15/17

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SLIDE 74

m n ≔        m n if m :: α β, n :: α λk. m λf . n λx. k f x

  • therwise

m n ≔        n m if n :: α β, m :: α λk. m λx. n λf . k x f

  • therwise

m n ≔        λx. m x ∧ n x if m :: α β, n :: α β λk. m (λx. n (λf . k (f x)))

  • therwise

Item Type Denotation rabbit e t rab hat e t hat in e e t in someu (e Dt) Ke λckg. {k x g′ | x ∈ De, T, g′ ∈ c x gu→x} theu K(eDt)Ke λkg. 1u (k someu) g 1u Fα λmg.          G if |Gν | = 1, where G = m g Gu = {g u | ·, g ∈ G} #

  • therwise

16/17

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SLIDE 75

the rabbit in the hat =

  • 1u [ ]

someu (λx. [ ]) x

  • [ ]

[ ] rab [ ] [ ] in

  • 1ν [ ]

someν (λy. [ ]) y

  • [ ]

[ ] hat

  • ⇒
  • ⇒

ë

  • 1u [ ]

someu (λx. [ ]) x

  • [ ]

[ ] rab [ ] [ ] in 1ν [ ] λg. {[ ] gν→y | hat y} y

  • ⇒

ë

  • 1u (1ν [ ])

someu (λxg. {[ ] gν→y | hat y}) rab x ∧ in y x

  • ⇒

ë

  • 1u (1ν [ ])

λg.

  • [ ] g

u→x ν→y

  • hat y, rab x, in y x
  • x
  • ë
  • 1u
  • 1ν
  • λg.
  • x, g

u→x ν→y

  • hat y, rab x, in y x

⋆ λg. [ ] g

u→x ν→y

x , where x = ιx: hat. ∃y. rab y ∧ in x y, y = ιy: rab. in x y

17/17