Przepiórkowski-inspired Quantification in TRALE...Przepiórkowski-inspired Quantiﬁcation in TRALE...

Przepiórkowski-inspired Quantificationin TRALE

Jonathan Khoo

jkhoo@sfs.uni-tuebingen.de

Grammar EngineeringSummer Semester 2006

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

Agenda

1 Background

2 Przepiórkowski 1998

3 Development of the Grammar

4 In Action

5 Summary

Agenda

1 Background

4 In Action

5 Summary

Quantifiers and Quantificational NPs

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

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 representthe 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 representthe ambiguity?

Quantifier Storage to the Rescue!

“Cooper Storage”As a sentence is parsed, quantifiers go into storage as they areencounteredThey can be retrieved appropriately when enough information

Goal: Represent all possibilities

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.

Development of Quantification in HPSG

Pollard and Sag (1994) (from Pollard and Yoo (1998))2666666666666664

signPHONOLOGY 〈every student〉

SYNSEM

2664LOCAL

"CATEGORY | HEAD nounCONTENT npro

#NONLOCAL nonlocal

3775QSTORE

oRETRIEVED 〈〉

37777777777777751 =[∀y |student(y)]

Development of Quantification in HPSG

Pollard and Yoo (1998)26666666666664

signPHONOLOGY list(phonstring)

SYNSEM

266664LOCAL

26664CATEGORY categoryCONTENT contentQSTORE set(quantifier)POOL set(quantifier)

37775377775

RETRIEVED list(quantifier)

37777777777775Fixed: Filler-gap and raising constructions

Agenda

1 Background

4 In Action

5 Summary

Simpler analysis: completely lexicalNo complex constraintsSemantics completely in CONTENT

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

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

Overview

(1.2a)

24content

QSTOREn

quant*o35

kkkkkkkSSSSSSS

psoa nom-obj quant

(1.2b)

2664word. . .

NEW-QUANTIFIERSn

quant*o

(1.3) word → Desc1 ∨ Desc2

(1.4) Desc1 =

2666664SS|LOC|CONT

"nom-obj ∨ quant

QSTORE 1

2664psoa

QSTORE 2

QUANTS 3

3775NEW-QUANTIFIERS 5

3777775where 1 = 5 ] union QSTOREs of selected arguments

4 = set of elements of 3

1 = 2 ] 4

(1.5) Desc2 =

264SS|LOC|CONT 1

ARG-ST

fi. . . ,

hSS|LOC|CONT 1

i, . . .

fl375Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44

Overview

(1.2a)

24content

QSTOREn

quant*o35

kkkkkkkSSSSSSS

psoa nom-obj quant

(1.2b)

2664word. . .

NEW-QUANTIFIERSn

quant*o

(1.4) Desc1 =

2666664SS|LOC|CONT

"nom-obj ∨ quant

QSTORE 1

2664psoa

QSTORE 2

QUANTS 3

1 = 2 ] 4

(1.5) Desc2 =

264SS|LOC|CONT 1

ARG-ST

fi. . . ,

hSS|LOC|CONT 1

i, . . .

Overview

(1.2a)

24content

QSTOREn

quant*o35

kkkkkkkSSSSSSS

psoa nom-obj quant

(1.2b)

2664word. . .

NEW-QUANTIFIERSn

quant*o

(1.4) Desc1 =

2666664SS|LOC|CONT

"nom-obj ∨ quant

QSTORE 1

2664psoa

QSTORE 2

QUANTS 3

1 = 2 ] 4

(1.5) Desc2 =

264SS|LOC|CONT 1

ARG-ST

fi. . . ,

hSS|LOC|CONT 1

i, . . .

Overview

(1.2a)

24content

QSTOREn

quant*o35

kkkkkkkSSSSSSS

psoa nom-obj quant

(1.2b)

2664word. . .

NEW-QUANTIFIERSn

quant*o

(1.4) Desc1 =

2666664SS|LOC|CONT

"nom-obj ∨ quant

QSTORE 1

2664psoa

QSTORE 2

QUANTS 3

1 = 2 ] 4

(1.5) Desc2 =

264SS|LOC|CONT 1

ARG-ST

fi. . . ,

hSS|LOC|CONT 1

i, . . .

Concepts

QSTORE filled from selected argumentsQSTORE accumulates quantifiers from QSTOREs of those membersof ARG-ST not raised from other arguments

ARGUMENT-STRUCTURE

Semantics-driven subcategorization frameDevolution of Semantics Principle

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

A unicorn appears to be approaching.ú�û9��Cþ

jk � � ¶ À ½EÄ�� O n ) Q,m<XZobxU\ANPX��m)m�m � O n N � vwa a a a a a a a a a bbbbbbbbbb

jk�� ¶ À ½EÄ�� O n ) Q�M� n M*R�� O�� O n N � � vwj��kl ·R¶ ¹�� O n ) Q��

m�m)m � O n N ç j��k �� À »�ÅL�M*N0OQP�R�� R4N�T��SUVrSP�R�M*N�� n��

v"!!w�QP('0prM�N*)A3n R4o~p_L�M��

v !!!!!!!!!!w

jk�� ¶ À ½{Ä�� O n ) mZX<obxU\�NPX��m�m�m � O n N � vwj��kl ·R¶ ¹�� O n ) m<X<obxU\�NPX��

m�m�m � O n N �j��k» � ¶¯·L�M*N0OQP�R�� n�� R� �P�R�M�N�P!�

K � »�º ¸V·R¶ »� n M*N � ` �

v"!!!!w�QP '0prM*N*) 3n R�oqprLsM"�#�

v"!!!!!!!!!!!!wÙ�ÚOÛ�å�Û�Ü7å¡Û�â ö à��y��Wã�â�å¡óIõyâ�óIå�Û�ã§Þ�ë#â�ÚIÞ�ã�â�å�Û�Û ö ÚIÞ�õ¡Ú#ß4óIã�âÝã�Ü7â�ÞÑã�á¥ñ5ú�û9�JxCþA@ � ÜØëIéh �0��*�4��£��Ù�ÚIÛuá�àØå¡ß�Û�å Þ�ë[â�å�à�éIóIõyÛ�ã�Ü_ò²óIÜØëLâ�Þ¾ônÛ�å�ÞÑë /�l s<; @ t ÜØëIé�Þ�ëIõyàØå�ä?àØå¡Ü7â�Û�ãÞÑâ ÞÑëLâ�à @ t > q iQl è²ÞÑÜ {§Û�ã¡õ ´ ú�û9�p;LþA��Ù�ÚIÞÑã�è7ÜØøÑóOÛ'ä?Û�å¡õyàCø�Ü7â�Û�ã â�àG�ØÛ�â�ÚOÛ�å ö ÞÑâ�Ú�â�ÚOÛö ÚOàCøÖÛ 1 q /?>l0/2> è7ÜØøÑóOÛ â�à+â�ÚIÛ'ß Ü< �Þ�ß ÜØø%äIå�àCB�Û�õyâ�ÞÖàCë�õyàCóOå¡â�Û�ã�ñ àØá§â�ÚOÛWî²Û�ß ÜØë��â�Þ�õ#í�å¼ÞÑëIõ�ÞÖänøÑÛG��î�ÞÑëIõyÛ'â�ÚIÛKã�ñ�ëIã�Û�ß2àØá,â�ÚIÞ�ã ß Ü< OÞÑß ÜØø�äIå�àCB�Û�õyâ�ÞÖàCë ÞÑã äIå¡Û�ã�Û�ë[â�ÞÑëh �0��*�4��~B°ã eUi�H ;¡t > ÿAâ�ÚnÞÑã,ò²óIÜØë[â�ÞÖônÛ�å¬ÞÑã,ÜØß ÜØø��CÜØß Ü7â�Û�éQÿ�Ü9�CÜØÞÑë5è²Þ�Ü {êÛ�ã�õ ´ ÿAâ�à0â�ÚOÛëIàCóIë�B°ã @ t > q iQl ��DêëIéQÿLÜ9�CÜØÞÑë õyàCóOå¡â�Û�ã�ñ�àØáQâ�ÚOÛêî²Û�ß ÜØë[â�ÞÑõ�í�å¡ÞÑënõ�ÞÖänøÖÛØÿCÞÖâ�Þ�ã�äIå�Û�ã�Û�ë[âàCë'â�ÚOÛ%$êí�B°ã"@ t > q iQl �

L�Û�â�óIã�ëOà ö øÑàLàG��Ü7â�â�ÚOÛ,â�å¡Û�Û¬ã�â�å¡óIõyâ�óIå�Û,õyàØå�å�Û�ã�ä?àCëIénÞÑë�4â�à0ú�û9�Ñû�Ü[þA�

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

A unicorn appears to be approaching. (bottom)

NP264phrasePHON 〈a unicorn〉SS 1

hLOC|CONT|QS

narrow 2 :26664psoaQSTORE {}QUANTS

ENUCL approach

wide 2 :26664psoa

QSTOREn

QUANTS 〈〉NUCL approach

llllllllllRRRRRRRRRR

V226664wordPHON 〈to〉SS

ˆLOC|CONT 2

˜ARG-ST

˙1 , 11

¸37775

VP3"phraseSS 11

ˆLOC|CONT 2

rrrrrrrrrr

LLLLLLLLLL

��

V326664wordPHON 〈be〉SS

ˆLOC|CONT 2

˜ARG-ST

˙1 , 10

¸37775

VP4"phraseSS 10

ˆLOC|CONT 2

#��

V4266664wordPHON 〈approaching〉SS

ˆLOC|CONT 2

˜NEW-QS{}ARG-ST

377775

A unicorn appears to be approaching. (top)

S»phraseSS|LOC|CONT 3

rrrrrrrrrr

LLLLLLLLLL

NP264phrasePHON 〈a unicorn〉SS 1

hLOC|CONT|QS

VP1»phraseSS|LOC|CONT 3

rrrrrrrrrr

LLLLLLLLLL

V1266664wordPHON 〈appears〉SS

ˆLOC|CONT 3

˜NEW-QS{}ARG-ST

˙1 , 12

377775

VP2"phraseSS 12

ˆLOC|CONT 2

#{{ jj

V2266664wordPHON 〈to〉SS

hLOC|CONT

oiARG-ST

D1 , 11

E377775

narrow 3 :2664psoaQSTORE {}QUANTS 〈〉NUCL appear

wide 3 :26664psoaQSTORE {}QUANTS

ENUCL appear

Agenda

1 Background

4 In Action

5 Summary

End Point

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

At First Glance...

(1.2a)

24content

QSTOREn

quant*o35

kkkkkkkSSSSSSS

psoa nom-obj quant

(1.2b)

2664word. . .

NEW-QUANTIFIERSn

quant*o

(1.4) Desc1 =

2666664SS|LOC|CONT

"nom-obj ∨ quant

QSTORE 1

2664psoa

QSTORE 2

QUANTS 3

1 = 2 ] 4

(1.5) Desc2 =

264SS|LOC|CONT 1

ARG-ST

fi. . . ,

hSS|LOC|CONT 1

i, . . .

Starting Point

Given this preliminary information, what would make sense?Choices

ScratchGroup Project GrammarCore Fragment from Richter (2005)

Why Core Fragment?ARG_ST set upBasic principles set up (Subcat, Semantics)Repurpose LEs

Preliminary Signature Changes

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

psoa (already present)visit_rel : VISITOR:ref VISITEE:ref

nom_objquant

Subsorts of quantifierforall_quantexists_quant

Preliminary Goals for the Theory

New quantifiers are placed in NEWQS

Move NEWQS to QSTORE

Amalgamate QSTOREs of selected argumentsPass CONTENT values upARG_ST captures valence informationSemantically vacuous words take CONTENT value from argumentRetrieve by moving quantifiers from QSTORE to QUANTS @ psoas

Fist Step: NPs

“a representative”“each customer”

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).

Lexical Entries for Quantifiers

How to represent quantifiers in the QSTORE?

In PS94:

264quantifierDET semdetRESTIND npro

375In Przepiórkowski: quant is a subsort of contentNo separate sort for quantifiers – makes it easier!

Instead of setting up QSTORE and NEWQS in the LE, do it via aprinciple

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)).

New Quantifier Principle

Sets the NEWQS and QSTORE for quantifiers

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

“A representative”

At this point, 2 resultsBoth 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-ComplementRule, and later, Head-Adjunct Rule

Thought about using something like the Functional PrepositionPrinciple 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))])).

Head Adjunct Rule for Quantifiers

New PSR by reversing HAhead_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_strucAdded cat:val:comps:e_list to the SAI phrase structure ruleto prevent application

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))]).

QSTORE Accumulation and Problems with theContent Principle

Make quantifier accumulation part of phrase structure rule?

Semantics principle says CONTENT of mother = CONTENT of hdtrBUT QSTORE involves ndtrConflict because parent QSTORE (and thus, CONTENT) differentfrom hdtr QSTORE

Possible Solutions to the Accumulation Problem

At this point...Continue and try to find a solutionSeparate the quantifiers from the “nucleus” inside CONTENT

Move the quantifiers from CONTENT

Have some sort of temporary storage (QSTORETEMP external toCONTENT)

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)

goalappend(QstoreA,QstoreC,Qcombo1),append(QstoreB,QstoreD,Qcombo2),append(Qcombo1,Qcombo2,Qcombo).

(phrase, daughters:(hc_struc)) *>(daughters:ndtr:synsem:loc:cont:qstore:QstoreA,qstoretemp:QstoreA).

New Direction: A Principled Decision

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

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))

goalappend(QstoreA,QstoreB,Qcombo).

Combinatorics

Six possibilitiesRealized QSTORE + QUANTS must be the sum of the QSTOREs ofthe selected arguments

QSTORE QUANTS〈∃∀〉〈〉〈∀∃〉〈〉〈∀〉〈∃〉〈∃〉〈∀〉〈〉〈∃∀〉〈〉〈∀∃〉

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)).

Elimination of Invalid Combinations

We need all combinations if there are two retrieval sitesAlso 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!

Agenda

1 Background

4 In Action

5 Summary

Agenda

1 Background

4 In Action

5 Summary

Summary

Quantifier storage viable option for quantifier semanticsSystem inspired by Przepiórkowski can be successfullyimplemented in TRALE

At least for “A representative visits each customer.”

Lessons learnedTRALE is intimidatingBut, comfort level ∝ time spent working on itLearn the syntaxPath errors won’t be caught; principles appear not to workDraw things out, keep notesOvergeneration is better than undergenerationChip away at the problem little by little

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.

Przepiórkowski-inspired Quantification in TRALE...Przepiórkowski-inspired Quantiﬁcation in TRALE...

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