Przepirkowski-inspired Quantification in TRALE Jonathan Khoo - - PowerPoint PPT Presentation

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Przepirkowski-inspired Quantification in TRALE Jonathan Khoo - - PowerPoint PPT Presentation

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Przepirkowski-inspired Quantification in TRALE Jonathan Khoo jkhoo@sfs.uni-tuebingen.de Grammar Engineering Summer Semester 2006 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 1 / 44 Agenda Background 1

slide-1
SLIDE 1

Przepiórkowski-inspired Quantification in TRALE

Jonathan Khoo

jkhoo@sfs.uni-tuebingen.de

Grammar Engineering Summer Semester 2006

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 1 / 44

slide-2
SLIDE 2

Agenda

1

Background

2

Przepiórkowski 1998

3

Development of the Grammar

4

In Action

5

Summary

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 2 / 44

slide-3
SLIDE 3

Agenda

1

Background

2

Przepiórkowski 1998

3

Development of the Grammar

4

In Action

5

Summary

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 3 / 44

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SLIDE 4

Quantifiers and Quantificational NPs

Representing quantifiers: every car a car ∀x(CAR(x)) ∃x(CAR(x)) Universal quantification Existential quantification

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 4 / 44

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SLIDE 5

Quantifier Scope Ambiguity A representative visits each customer.

There is a different representative for each customer. There is one representative for all customers.

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 5 / 44

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SLIDE 6

Quantifier Scope Ambiguity A representative visits each customer.

There is a different representative for each customer. ∀y(CUSTOMER(y) → ∃x(REPRESENTATIVE(x) ∧ VISITS(x, y))) There is one representative for all customers. ∃x(REPRESENTATIVE(x) ∧ ∀y(CUSTOMER(y) → VISITS(x, y))) Given that we only have one syntactic structure, how can we represent the ambiguity?

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 5 / 44

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SLIDE 7

Quantifier Storage to the Rescue!

“Cooper Storage” As a sentence is parsed, quantifiers go into storage as they are encountered They can be retrieved appropriately when enough information Goal: Represent all possibilities

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 6 / 44

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SLIDE 8

Quantifier Scope Ambiguity A unicorn appears to be approaching.

A unicorn appears to be approaching

may not exist (2)

  • exists (1)
  • .

1

Something appears to be approaching, and it is a unicorn.

2

Something appears to be approaching, and it appears to be a unicorn.

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 7 / 44

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SLIDE 9

Development of Quantification in HPSG

Pollard and Sag (1994) (from Pollard and Yoo (1998))

2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 sign

PHONOLOGY

every student

SYNSEM

2 6 6 4

LOCAL

"

CATEGORY | HEAD

noun

CONTENT

npro #

NONLOCAL

nonlocal 3 7 7 5

QSTORE

n

1

  • RETRIEVED
  • 3

7 7 7 7 7 7 7 7 7 7 7 7 7 7 5

1 =[∀y|student(y)] Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 8 / 44

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SLIDE 10

Development of Quantification in HPSG

Pollard and Yoo (1998)

2 6 6 6 6 6 6 6 6 6 6 6 6 4 sign

PHONOLOGY

list(phonstring)

SYNSEM

2 6 6 6 6 4

LOCAL

2 6 6 6 4

CATEGORY

category

CONTENT

content

QSTORE

set(quantifier)

POOL

set(quantifier) 3 7 7 7 5 3 7 7 7 7 5

RETRIEVED

list(quantifier) 3 7 7 7 7 7 7 7 7 7 7 7 7 5

Fixed: Filler-gap and raising constructions

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 9 / 44

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SLIDE 11

Agenda

1

Background

2

Przepiórkowski 1998

3

Development of the Grammar

4

In Action

5

Summary

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 10 / 44

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SLIDE 12

Fixes

Simpler analysis: completely lexical

No complex constraints Semantics completely in CONTENT

Works with traceless extractions [ARG-ST] PY: Retrieval at all psoas → spurious ambiguities [word restriction]

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 11 / 44

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SLIDE 13

Spurious Ambiguities in PY

Retrievals at VP2, VP3, VP4, and V4 yield the same reading

Figure:

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 12 / 44

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SLIDE 14

Overview

(1.2a) 2 4 content

QSTORE

n quant*

  • 3

5

  • psoa

nom-obj quant (1.2b) 2 6 6 4 word . . .

NEW-QUANTIFIERS

n quant*

  • 3

7 7 5 (1.3) word → Desc1 ∨ Desc2 (1.4) Desc1 = 2 6 6 6 6 6 4

SS|LOC|CONT

" nom-obj ∨ quant

QSTORE 1

# ∨ 2 6 6 4 psoa

QSTORE 2 QUANTS 3

3 7 7 5

NEW-QUANTIFIERS 5

3 7 7 7 7 7 5 where

1 = 5 ⊎ union QSTOREs of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4

(1.5) Desc2 = 2 6 4

SS|LOC|CONT 1 ARG-ST

fi . . . , h

SS|LOC|CONT 1

i , . . . fl 3 7 5

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44

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SLIDE 15

Overview

(1.2a) 2 4 content

QSTORE

n quant*

  • 3

5

  • psoa

nom-obj quant (1.2b) 2 6 6 4 word . . .

NEW-QUANTIFIERS

n quant*

  • 3

7 7 5 (1.3) word → Desc1 ∨ Desc2 (1.4) Desc1 = 2 6 6 6 6 6 4

SS|LOC|CONT

" nom-obj ∨ quant

QSTORE 1

# ∨ 2 6 6 4 psoa

QSTORE 2 QUANTS 3

3 7 7 5

NEW-QUANTIFIERS 5

3 7 7 7 7 7 5 where

1 = 5 ⊎ union QSTOREs of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4

(1.5) Desc2 = 2 6 4

SS|LOC|CONT 1 ARG-ST

fi . . . , h

SS|LOC|CONT 1

i , . . . fl 3 7 5

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44

slide-16
SLIDE 16

Overview

(1.2a) 2 4 content

QSTORE

n quant*

  • 3

5

  • psoa

nom-obj quant (1.2b) 2 6 6 4 word . . .

NEW-QUANTIFIERS

n quant*

  • 3

7 7 5 (1.3) word → Desc1 ∨ Desc2 (1.4) Desc1 = 2 6 6 6 6 6 4

SS|LOC|CONT

" nom-obj ∨ quant

QSTORE 1

# ∨ 2 6 6 4 psoa

QSTORE 2 QUANTS 3

3 7 7 5

NEW-QUANTIFIERS 5

3 7 7 7 7 7 5 where

1 = 5 ⊎ union QSTOREs of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4

(1.5) Desc2 = 2 6 4

SS|LOC|CONT 1 ARG-ST

fi . . . , h

SS|LOC|CONT 1

i , . . . fl 3 7 5

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44

slide-17
SLIDE 17

Overview

(1.2a) 2 4 content

QSTORE

n quant*

  • 3

5

  • psoa

nom-obj quant (1.2b) 2 6 6 4 word . . .

NEW-QUANTIFIERS

n quant*

  • 3

7 7 5 (1.3) word → Desc1 ∨ Desc2 (1.4) Desc1 = 2 6 6 6 6 6 4

SS|LOC|CONT

" nom-obj ∨ quant

QSTORE 1

# ∨ 2 6 6 4 psoa

QSTORE 2 QUANTS 3

3 7 7 5

NEW-QUANTIFIERS 5

3 7 7 7 7 7 5 where

1 = 5 ⊎ union QSTOREs of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4

(1.5) Desc2 = 2 6 4

SS|LOC|CONT 1 ARG-ST

fi . . . , h

SS|LOC|CONT 1

i , . . . fl 3 7 5

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44

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SLIDE 18

Concepts

QSTORE filled from selected arguments

QSTORE accumulates quantifiers from QSTOREs of those members

  • f ARG-ST not raised from other arguments

ARGUMENT-STRUCTURE

Semantics-driven subcategorization frame

Devolution of Semantics Principle

“The CONTENT value of a phrase is token-identical to that of the head daughter.” (PS94)

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 14 / 44

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SLIDE 19

A unicorn appears to be approaching.

ú❾û✾✁❈þ ❥ ❦ ✚ ✂ ➯ ➚ ➼❊➘ ✄✆☎ ❖ ♥ ✮ ◗✱♠❁❳❩♦❜①❯❭❆◆P❳✞✝ ♠✮♠✒♠ ✝ ❖ ♥ ◆ ✗ ✈ ✇ ❛ ❛ ❛ ❛ ❛ ❛ ❛ ❛ ❛ ❛ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❥ ❦✟✚ ✂ ➯ ➚ ➼❊➘ ✄✟☎ ❖ ♥ ✮ ◗✠✝ ▼☛✡ ♥ ▼✯❘✟☞ ✌ ✍ ✆✛❖✞✝✟✄ ✝ ❖ ♥ ◆ ✛ ✎ ✈ ✇ ❥ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ❦ ❧ ➲❘➯ ➵ ✄✟☎ ❖ ♥ ✮ ◗✏✝ ♠✒♠✮♠ ✝ ❖ ♥ ◆ ç ❥ ✂ ✂ ❦ ✓✖✕ ➚ ➺✑➴ ▲✏▼✯◆✵❖◗P✚❘✒✑ ✛ ✓ ✔ ❘✹◆☞❚✖✕✘✗➀❙❯❱r❙ P✚❘✕▼✯◆✚✙ ♥✛✔ ✗ ✈✧✦ ✦ ✇ ✢◗P✭✬✵♣r▼✝◆✯✮❆✸ ♥ ❘✹♦⑦♣❴▲✏▼✜✑ ✛ ✓ ✈ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✇ ❥❦✞✚ ✂ ➯ ➚ ➼④➘ ✄✟☎ ❖ ♥ ✮ ♠❩❳❁♦❜①❯❭☛◆P❳✢✝ ♠✒♠✒♠ ✝ ❖ ♥ ◆ ✗ ✈✇ ❥ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ❦ ❧ ➲❘➯ ➵ ✄✟☎ ❖ ♥ ✮ ♠❁❳❁♦❜①❯❭☛◆P❳✢✝ ♠✒♠✒♠ ✝ ❖ ♥ ◆ ✗ ❥ ✂ ✂ ✂ ✂ ❦ ➺ ✚ ➯➥➲ ▲✏▼✯◆✵❖◗P✚❘✣✑ ✛ ✓ ✙ ♥✤✔ ❘✘✥ ✤ P✚❘✕▼✝◆✚P✦✑ ❑ ✕ ➺✁➸ ➳❱➲❘➯ ➺ ✙ ♥ ▼✯◆ ✤ ❵ ✓ ✈✧✦ ✦ ✦ ✦ ✇ ✢◗P ✬✵♣r▼✯◆✯✮ ✌ ✸ ♥ ❘✛♦q♣r▲s▼✧✑★✓ ✈✧✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✇ Ù➇Ú❖Û✑å➄Û✟Ü✼å→Û✟â ö à➏✒②✑✛☎✁❲ã➎â➎å→ó■õ②â➄ó■å➄Û⑧ã➜Þ➐ë★â➄Ú■Þ➐ã✝â➎å➄Û✑Û ö Ú■Þ➐õ→Ú★ß✹ó■ã➎âÝã➄Ü✼â➄ÞÑã➄á➙ñ✺ú❾û✾❏①❈þ❆❅ ☛ ÜØë■é ❤ ✖✵✔✣✓✯✑✹☎✍✖↔✖Ù✝Ú■Û✉á➁àØå→ß✜Û✑å Þ➐ë❬â➎å➄à➓é■ó■õ②Û⑧ã✜Ü❴ò➨ó■ÜØë▲â➄Þ➽ô♥Û✑å✜ÞÑë ✴➅❧ s❁❀ ❅ t ÜØë■é✖Þ➐ë■õ②àØå➄ä❄àØå→Ü✼â➎Û⑧ã ÞÑâ ÞÑë▲â➎à ❅ t ❃ q ✐◗❧ è➨ÞÑÜ ④➜Û⑧ã→õ ➫ ú❾û✾♣❀▲þ❆❷Ù➇Ú■ÞÑã✜è✼ÜØøÑó❖Û✬ä❄Û✑å→õ②à❈ø➐Ü✼â➎Û⑧ã â➎à●☎ØÛ✑â➄Ú❖Û✑å ö ÞÑâ➄Ú✖â➄Ú❖Û ö Ú❖à❈øÖÛ ✶ q ✴❄❃✡❧✵✴✷❃ è✼ÜØøÑó❖Û â➎à✰â➄Ú■Û✬ß Ü❁✌➓Þ➐ß ÜØø✪ä■å➄à❈❇➎Û⑧õ②â➄ÞÖà❈ë✚õ②à❈ó❖å→â➎Û⑧ã➎ñ✥àØá➜â➄Ú❖Û❲î➨Û⑧ß ÜØë✟✞ â➄Þ➐õ★í☞å➻ÞÑë■õ✑ÞÖä♥øÑÛ●❷î➓ÞÑë■õ②Û✬â➄Ú■Û❑ã➎ñ➓ë■ã➎Û⑧ß✷àØá✱â➄Ú■Þ➐ã ß Ü❁✌❖ÞÑß ÜØø➇ä■å➄à❈❇➎Û⑧õ②â➄ÞÖà❈ë ÞÑã ä■å→Û⑧ã➎Û⑧ë❬â➋ÞÑë ❤ ✖✵✔✣✓✯✑✹☎✍✖⑦❇➦ã ❡❯✐✒❍ ❀→t ❃ ÿ❆â➄Ú♥ÞÑã✱ò➨ó■ÜØë❬â➄ÞÖô♥Û✑å➡ÞÑã✱ÜØß ÜØø✆☎❈ÜØß Ü✼â➎Û⑧é◗ÿ☞Ü✾☎❈ÜØÞÑë✺è➨Þ➐Ü ④êÛ⑧ã➄õ ➫ ÿ❆â➎à✵â➄Ú❖Û ë■à❈ó■ë✎❇➦ã ❅ t ❃ q ✐◗❧ ✄❉êë■é◗ÿ▲Ü✾☎❈ÜØÞÑë õ②à❈ó❖å→â➎Û⑧ã➎ñ✜àØá◗â➄Ú❖Ûêî➨Û⑧ß ÜØë❬â➄ÞÑõ➇í☞å→ÞÑë♥õ✑ÞÖä♥øÖÛØÿ❈ÞÖâ☞Þ➐ã☞ä■å➄Û⑧ã➄Û⑧ë❬â à❈ë✬â➄Ú❖Û✪✩êí✤❇➦ã✧❅ t ❃ q ✐◗❧
  • ▲➅Û✑â➇ó■ã➇ë❖à
ö øÑà▲à●☞➋Ü✼â✝â➄Ú❖Û✱â➎å→Û✑Û➡ã➎â➎å→ó■õ②â➄ó■å➄Û✱õ②àØå➄å➄Û⑧ã➎ä❄à❈ë■é♥ÞÑë✡☎✹â➎à✵ú❾û✾Ñû✑Ü❬þ❆ ❀

Figure:

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 15 / 44

slide-20
SLIDE 20

A unicorn appears to be approaching. (bottom)

NP 2 6 4 phrase

PHON a unicorn SS 1

h

LOC|CONT|QS

n

4

  • i

3 7 5 narrow 2 : 2 6 6 6 4 psoa

QSTORE {} QUANTS

D

4

E

NUCL

approach 3 7 7 7 5 wide 2 : 2 6 6 6 4 psoa

QSTORE

n

4

  • QUANTS

NUCL

approach 3 7 7 7 5

  • V2

2 6 6 6 4 word

PHON to SS

ˆ

LOC|CONT 2 ˜ ARG-ST

˙

1 , 11 ¸

3 7 7 7 5

  • VP3

" phrase

SS 11ˆ LOC|CONT 2 ˜

#

  • V3

2 6 6 6 4 word

PHON be SS

ˆ

LOC|CONT 2 ˜ ARG-ST

˙

1 , 10 ¸

3 7 7 7 5

  • VP4

" phrase

SS 10ˆ LOC|CONT 2 ˜

#

  • V4

2 6 6 6 6 4 word

PHON approaching SS

ˆ

LOC|CONT 2 ˜ NEW-QS{} ARG-ST

˙

1 ¸

3 7 7 7 7 5

  • Jonathan Khoo (jkhoo@sfs)

Quantification & TRALE Grammar Engineering SS06 16 / 44

slide-21
SLIDE 21

A unicorn appears to be approaching. (top)

S »phrase

SS|LOC|CONT 3

–

  • NP

2 6 4 phrase

PHON a unicorn SS 1

h

LOC|CONT|QS

˘

4 ¯

i 3 7 5 VP1 »phrase

SS|LOC|CONT 3

–

  • V1

2 6 6 6 6 4 word

PHON appears SS

ˆ

LOC|CONT 3 ˜ NEW-QS{} ARG-ST

˙

1 , 12 ¸

3 7 7 7 7 5

  • VP2

" phrase

SS 12ˆ LOC|CONT 2 ˜

#

  • V2

2 6 6 6 6 4 word

PHON to SS

h

LOC|CONT

n

2

  • i

ARG-ST

D

1 , 11

E 3 7 7 7 7 5 narrow 3 : 2 6 6 4 psoa

QSTORE {} QUANTS NUCL

appear 3 7 7 5 wide 3 : 2 6 6 6 4 psoa

QSTORE {} QUANTS

D

4

E

NUCL

appear 3 7 7 7 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 17 / 44

slide-22
SLIDE 22

Agenda

1

Background

2

Przepiórkowski 1998

3

Development of the Grammar

4

In Action

5

Summary

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 18 / 44

slide-23
SLIDE 23

End Point

End Points

Primary goal: “A representative visits each customer.” (two quantifiers, one retrieval site) Secondary goal: “A unicorn appears to be approaching.” (one quantifier, two retrieval sites)

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 19 / 44

slide-24
SLIDE 24

At First Glance...

(1.2a) 2 4 content

QSTORE

n quant*

  • 3

5

  • psoa

nom-obj quant (1.2b) 2 6 6 4 word . . .

NEW-QUANTIFIERS

n quant*

  • 3

7 7 5 (1.3) word → Desc1 ∨ Desc2 (1.4) Desc1 = 2 6 6 6 6 6 4

SS|LOC|CONT

" nom-obj ∨ quant

QSTORE 1

# ∨ 2 6 6 4 psoa

QSTORE 2 QUANTS 3

3 7 7 5

NEW-QUANTIFIERS 5

3 7 7 7 7 7 5 where

1 = 5 ⊎ union QSTOREs of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4

(1.5) Desc2 = 2 6 4

SS|LOC|CONT 1 ARG-ST

fi . . . , h

SS|LOC|CONT 1

i , . . . fl 3 7 5

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 20 / 44

slide-25
SLIDE 25

Starting Point

Given this preliminary information, what would make sense? Choices

Scratch Group Project Grammar Core Fragment from Richter (2005)

Why Core Fragment?

ARG_ST set up Basic principles set up (Subcat, Semantics) Repurpose LEs

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 21 / 44

slide-26
SLIDE 26

Preliminary Signature Changes

Sign level of word: NEWQS { }, CR boolean Attribute of content: QSTORE { } Subsorts of content

psoa (already present)

visit_rel: VISITOR:ref VISITEE:ref

nom_obj quant

Subsorts of quantifier

forall_quant exists_quant

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 22 / 44

slide-27
SLIDE 27

Preliminary Goals for the Theory

New quantifiers are placed in NEWQS Move NEWQS to QSTORE Amalgamate QSTOREs of selected arguments Pass CONTENT values up

ARG_ST captures valence information

Semantically vacuous words take CONTENT value from argument Retrieve by moving quantifiers from QSTORE to QUANTS @ psoas

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 23 / 44

slide-28
SLIDE 28

Fist Step: NPs

“a representative” “each customer”

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 24 / 44

slide-29
SLIDE 29

Lexical Entries for the Nouns

Use “Mary” as the basis for “representative” and “customer”

representative ~~> (synsem:loc:(cat:head:(noun, pred:minus), cont:(nom_obj,index:(ref, num:sg, pers:third, gen:neut))), arg_st:e_list). Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 25 / 44

slide-30
SLIDE 30

Lexical Entries for Quantifiers

How to represent quantifiers in the QSTORE?

In PS94:

2 6 4 quantifier

DET

semdet

RESTIND

npro 3 7 5

In Przepiórkowski: quant is a subsort of content No separate sort for quantifiers – makes it easier! Instead of setting up QSTORE and NEWQS in the LE, do it via a principle

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 26 / 44

slide-31
SLIDE 31

Lexical Entries for Quantifiers

Very simple: a ~~> (word, synsem:loc:(cont:(quant, det:exists_quant), cat:val:comps:e_list)). each ~~> (word, synsem:loc:(cont:(quant, det:forall_quant), cat:val:comps:e_list)).

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 27 / 44

slide-32
SLIDE 32

New Quantifier Principle

Sets the NEWQS and QSTORE for quantifiers

(word, synsem:loc:cont:(quant)) *> (synsem:Synsem, newqs:[Synsem], synsem:loc:cont:qstore:[Synsem]).

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 28 / 44

slide-33
SLIDE 33

“A representative”

At this point, 2 results Both take the quantifier as the CONTENT One has the noun in SUBJ, the other in COMPS

Ran into trouble with Subj-Aux Inversion and Head-Complement Rule, and later, Head-Adjunct Rule

Thought about using something like the Functional Preposition Principle to set SUBJ and COMPS:

(word, phon:ne_list, synsem:loc:cat:head:(prep, pform:non_lexical)) *> (synsem:loc:(cat:(head:(mod:none,pred:minus)), cont:Cont), arg_st:([(loc:(cat:val:(subj:[],comps:[]), cont:Cont))]) ). Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 29 / 44

slide-34
SLIDE 34

Head Adjunct Rule for Quantifiers

New PSR by reversing HA

head_adjunct_rule_q ## (phrase, synsem:loc:cat:val:(subj:List, comps:e_list), daughters:(qh_struc, hdtr:Hdtr, ndtr:Ndtr)) ===> cat> (Ndtr, synsem:loc:cat:(head:mod:Synsem, val:(subj:e_list, comps:e_list))), cat> (Hdtr, synsem:(Synsem, loc:(cat:val:(subj:List, comps:e_list), cont:nom_obj))).

New subsort of const_struc: qh_struc Added cat:val:comps:e_list to the SAI phrase structure rule to prevent application

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 30 / 44

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SLIDE 35

Lexical Entry for the Verb

Use “likes” as the basis for “visits”

visits ~~> (synsem:loc:(cat:(head:(verb, vform: fin, pred: plus, aux: minus), val:subj:[(loc:cont:(psoa;index:(pers:third, num:sg)))]), cont:(visit_rel, visitor:Index1, visitee:Index2)), arg_st:[(loc:(cat:(head:noun, val:(subj:e_list, comps:e_list)), cont:index:Index1)), (loc:(cat:(head:noun, val:(subj:e_list, comps:e_list)), cont:index:Index2))]). Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 31 / 44

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SLIDE 36

QSTORE Accumulation and Problems with the

Content Principle

Make quantifier accumulation part of phrase structure rule? Semantics principle says CONTENT of mother = CONTENT of hdtr BUT QSTORE involves ndtr Conflict because parent QSTORE (and thus, CONTENT) different from hdtr QSTORE

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 32 / 44

slide-37
SLIDE 37

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 33 / 44

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SLIDE 38

Possible Solutions to the Accumulation Problem

At this point... Continue and try to find a solution Separate the quantifiers from the “nucleus” inside CONTENT Move the quantifiers from CONTENT Have some sort of temporary storage (QSTORETEMP external to

CONTENT)

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44

slide-39
SLIDE 39

Possible Solutions to the Accumulation Problem

At this point... Continue and try to find a solution Separate the quantifiers from the “nucleus” inside CONTENT Move the quantifiers from CONTENT Have some sort of temporary storage (QSTORETEMP external to

CONTENT)

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44

slide-40
SLIDE 40

Possible Solutions to the Accumulation Problem

At this point... Continue and try to find a solution Separate the quantifiers from the “nucleus” inside CONTENT Move the quantifiers from CONTENT Have some sort of temporary storage (QSTORETEMP external to

CONTENT)

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44

slide-41
SLIDE 41

Possible Solutions to the Accumulation Problem

At this point... Continue and try to find a solution Separate the quantifiers from the “nucleus” inside CONTENT Move the quantifiers from CONTENT Have some sort of temporary storage (QSTORETEMP external to

CONTENT)

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44

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SLIDE 42

Digging a Hole

% Quantifier Accumulation and Distribution Principle for psoa (phrase, daughters:(hs_struc)) *> (daughters:ndtr:synsem:loc:cont:qstore:QstoreA, daughters:hdtr:synsem:loc:cont:qstore:QstoreB, daughters:ndtr:qstoretemp:QstoreC, daughters:hdtr:qstoretemp:QstoreD, qstoretemp:Qcombo) goal append(QstoreA,QstoreC,Qcombo1), append(QstoreB,QstoreD,Qcombo2), append(Qcombo1,Qcombo2,Qcombo). (phrase, daughters:(hc_struc)) *> (daughters:ndtr:synsem:loc:cont:qstore:QstoreA, qstoretemp:QstoreA).

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 35 / 44

slide-43
SLIDE 43

New Direction: A Principled Decision

Move from using DTRS to having principles on words only Returns back to original Przepiórkowski theory

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 36 / 44

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SLIDE 44

First Version of Quantifier Accumulation Principle

(word, synsem:loc:(cont:psoa, cat:val:(subj:ne_list,comps:ne_list)) ) *> (synsem:loc:(cat:val:(subj:[(loc:cont:qstore:QstoreA)|Rest1], comps:[(loc:cont:qstore:QstoreB)|Rest2]), cont:qstore:Qcombo)) goal append(QstoreA,QstoreB,Qcombo).

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 37 / 44

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SLIDE 45

Combinatorics

Six possibilities Realized QSTORE + QUANTS must be the sum of the QSTOREs of the selected arguments

QSTORE QUANTS

∃∀

  • ∀∃
  • ∀

∃ ∃ ∀

  • ∃∀
  • ∀∃

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 38 / 44

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SLIDE 46

Final Quantifier Accumulation Principle

Three parts, (ne_list/ne_list, e_list/ne_list, ne_list/e_list) Retrieval (all combinations from QSTORE to QUANTS)

(word, synsem:loc:(cont:psoa, cat:(val:(subj:ne_list,comps:ne_list), head:aux:minus)) ) *> (synsem:loc:(cat:val:(subj:[(loc:cont:qstore:QstoreA)|Rest1], comps:[(loc:cont:qstore:QstoreB)|Rest2]), cont:(qstore:Qstore,quants:Quants))) goal ((append(QstoreA,QstoreB,TotalQs);append(QstoreB,QstoreA,TotalQs)), append(Qstore,Quants,TotalQs)).

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 39 / 44

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SLIDE 47

Elimination of Invalid Combinations

We need all combinations if there are two retrieval sites Also need to ensure that QSTORE empty at the top of the tree

head_subject_rule ## (phrase, synsem:loc:(cat:(val:(subj:e_list, comps:e_list)), cont:qstore:e_list), daughters:(hs_struc, hdtr:Hdtr, ndtr:Ndtr)) ===> cat> (Ndtr, synsem:Synsem), cat> (Hdtr, synsem:loc:(cat:val:(subj:[Synsem], comps:e_list), cont:psoa)).

...2 results!

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 40 / 44

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SLIDE 48

Agenda

1

Background

2

Przepiórkowski 1998

3

Development of the Grammar

4

In Action

5

Summary

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 41 / 44

slide-49
SLIDE 49

Agenda

1

Background

2

Przepiórkowski 1998

3

Development of the Grammar

4

In Action

5

Summary

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 42 / 44

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SLIDE 50

Summary

Quantifier storage viable option for quantifier semantics System inspired by Przepiórkowski can be successfully implemented in TRALE

At least for “A representative visits each customer.”

Lessons learned

TRALE is intimidating But, comfort level ∝ time spent working on it Learn the syntax Path errors won’t be caught; principles appear not to work Draw things out, keep notes Overgeneration is better than undergeneration Chip away at the problem little by little

Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 43 / 44

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SLIDE 51

Questions?

References Carl Pollard and Ivan A. Sag. Head-Driven Phrase Structure Grammar. University of Chicago Press and CSLI Publications, Chicago, Illinois, 1994. Carl Pollard and Eun Jung Yoo. A unified theory of scope for quantifiers and wh-phrases.

  • J. Linguistics, 34:415–445, 1998.

Adam Przepiórkowski. Quantifiers, adjuncts as complements and scope ambiguities. Unpublished manuscript, December 1997. Adam Przepiórkowski. ‘A Unified Theory of Scope’ revisited: Quantifier retrieval without spurious ambiguities. In Gosse Bouma, Geert-Jan Kruijff, and Richard Oehrle, editors, Proceedings of FHCG’98, 1998. To appear. Frank Richter. A Web-based Course in Grammar Formalisms and Parsing. http://milca.sfs.uni-tuebingen.de/A4/Course/PDF/gramandpars.pdf, 2005. Electronic textbook. Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 44 / 44