przepiórkowski-inspired quantification in trale...przepiórkowski-inspired quantification in trale...
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Przepiórkowski-inspired Quantificationin TRALE
Jonathan Khoo
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 2 / 44
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
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
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?
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 5 / 44
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?
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 5 / 44
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 6 / 44
Quantifier Scope Ambiguity
A unicorn appears to be approaching.
A unicorn appears to be approaching
may not exist (2)
OO
exists (1)
OO .
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
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
n1
oRETRIEVED 〈〉
37777777777777751 =[∀y |student(y)]
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 8 / 44
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 9 / 44
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
Fixes
Simpler analysis: completely lexicalNo complex constraintsSemantics 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
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
3775
(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
3775
(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
3775
(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
3775
(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
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)
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 14 / 44
A unicorn appears to be approaching.ú�û9���Cþ
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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
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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"�#�
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;
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
n4
oi375
narrow 2 :26664psoaQSTORE {}QUANTS
D4
ENUCL approach
37775
wide 2 :26664psoa
QSTOREn
4o
QUANTS 〈〉NUCL approach
37775
llllllllllRRRRRRRRRR
V226664wordPHON 〈to〉SS
ˆLOC|CONT 2
˜ARG-ST
˙1 , 11
¸37775
33
VP3"phraseSS 11
ˆLOC|CONT 2
#
rrrrrrrrrr
LLLLLLLLLL
��
V326664wordPHON 〈be〉SS
ˆLOC|CONT 2
˜ARG-ST
˙1 , 10
¸37775
GG
VP4"phraseSS 10
ˆLOC|CONT 2
#��
V4266664wordPHON 〈approaching〉SS
ˆLOC|CONT 2
˜NEW-QS{}ARG-ST
˙1
¸
377775
jj
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 16 / 44
A unicorn appears to be approaching. (top)
S»phraseSS|LOC|CONT 3
–
rrrrrrrrrr
LLLLLLLLLL
NP264phrasePHON 〈a unicorn〉SS 1
hLOC|CONT|QS
˘4
i375
VP1»phraseSS|LOC|CONT 3
–
oo
rrrrrrrrrr
LLLLLLLLLL
V1266664wordPHON 〈appears〉SS
ˆLOC|CONT 3
˜NEW-QS{}ARG-ST
˙1 , 12
¸
377775
55
VP2"phraseSS 12
ˆLOC|CONT 2
#{{ jj
V2266664wordPHON 〈to〉SS
hLOC|CONT
n2
oiARG-ST
D1 , 11
E377775
narrow 3 :2664psoaQSTORE {}QUANTS 〈〉NUCL appear
3775
wide 3 :26664psoaQSTORE {}QUANTS
D4
ENUCL appear
37775
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 17 / 44
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
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)
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 19 / 44
At First Glance...
(1.2a)
24content
QSTOREn
quant*o35
kkkkkkkSSSSSSS
psoa nom-obj quant
(1.2b)
2664word. . .
NEW-QUANTIFIERSn
quant*o
3775
(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 20 / 44
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 21 / 44
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 22 / 44
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 23 / 44
Fist Step: NPs
“a representative”“each customer”
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 24 / 44
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
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 26 / 44
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
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
“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))])).
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 29 / 44
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 30 / 44
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
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 32 / 44
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 33 / 44
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)
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44
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)
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44
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)
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44
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)
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 34 / 44
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).
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 35 / 44
New Direction: A Principled Decision
Move from using DTRS to having principles on words onlyReturns back to original Przepiórkowski theory
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 36 / 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))
goalappend(QstoreA,QstoreB,Qcombo).
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 37 / 44
Combinatorics
Six possibilitiesRealized QSTORE + QUANTS must be the sum of the QSTOREs ofthe selected arguments
QSTORE QUANTS〈∃∀〉 〈〉〈∀∃〉 〈〉〈∀〉 〈∃〉〈∃〉 〈∀〉〈〉 〈∃∀〉〈〉 〈∀∃〉
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 38 / 44
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
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!
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 40 / 44
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
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
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
Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 43 / 44
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