Grammatical Relations and Lexical Functional Grammar

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Grammatical Relationsand Lexical Functional
Grammar

• Grammar Formalisms
• Spring Term 2004

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Grammatical Relations

• Subject
• Sam ate a sandwich.
• A sandwich was eaten by Sam.
• Direct object
• Sam ate a sandwich.
• Sue gave Sam a book.
• Sue gave a book to Sam.
• Others that we will define later

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Grammatical Relations in Grammar Formalisms

• Tree Adjoining Grammar
• Subject is defined structurally first NP
  daughter under S
• Object is defined structurally NP that is a
  sister to V
• But TAG output can be mapped to a dependency
  grammar tree that includes subject and object.
• Categorial Grammar
• Grammatical relations are defined structurally if
  at all.
• Head Driven Phrase Structure Grammar
• Subject is defined indirectly as the first
  element on the verbs subcategorization list.
• Lexical Functional Grammar
• Grammatical relations are labelled explicitly in
  a feature structure.

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Motivation for Grammatical Relations
Subject-Verb Agreement

• Sam likes sandwiches.
• Sam like sandwiches.
• The boys like sandwiches.
• The boys likes sandwiches.
• Hypothesis 1 The verb agrees with the agent.
• Hypothesis 2 The verb agrees with the first NP.
• Hypothesis 3 The verb agrees with the NP that is
  a sister of VP.
• Hypothesis 4 The verb agrees with the subject.
• Vacuous unless we have a definition or test for
  subjecthood.

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Checking the hypotheses

• Hypothesis 1
• Can you think of a counterexample in English.?
• Hypothesis 2
• Can you think of a counterexample in English?
• Can you think of a counterexample in another
  language that has subject-verb agreeement?
• (not Japanese or Chinese)

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Some differences between English and Warlpiri
(Australia)
Aux
V NP
The two small children are chasing that
dog.
S
NP AUX V
NP NP NP
Wita-jarra-rlu ka-pala
wajili-pi-nyi yalumpu kurdu-jarra-rlu maliki.
Small-DU-ERG pres-3duSUBJ chase-NPAST
that.ABS child-DU-ERG dog.ABS
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Some Definitions

• Case marking different word form depending on
  the grammatical relation
• She ate a sandwich. (nominative case marking
  subject)
• Her ate a sandwich.
• Sam saw her. (accusative or objective case
  marking object)
• Sam saw she.
• Ergative case marking
• Marks the subject, but only if the verb is
  transitive (has a direct object).
• Absolutive case marking
• Marks the subject, but only if the verb is
  intransitive.
• Also marks the direct object.
• English has nominative and accusative case
  markers on pronouns.
• English does not have ergative or absolutive case
  marking.

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Possible word orders in Warlpiri that are not
possible in English

• The two small are chasing that children dog.
• The two small are dog chasing that children.
• Chasing are the two small that dog children.
• That are children chasing the two small dog.

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Checking the hypotheses

• Hypothesis 2
• Does it work for Warlpiri?
• Hypothesis 3
• Does it work for Warlpiri?

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English and Warlpiri Under Hypothesis 3
Deep structure
English
Surface Structure
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English and Warlpiri under Hypothesis 3
S
VP
VP
NP

Deep structure
Aux V NP
S
Warlpiri
NP S
AUX S
S NP
Surface Structure
e
e
e
e
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English and Warlpiri under Hypothesis 3
S
VP
Deep structure
VP
NP

Aux V NP
S
Warlpiri
Adjunctions represent the real word order
NP S
AUX S
Remnants of the original tree represent
gramamtical relations
S NP
Empty categories represent semantic roles
Surface Structure
e
e
e
e
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English and Warlpiri under Hypothesis 4
Functional structure represents grammatical
relations and semantic roles
Constituent structure represents word order and
grouping of words into constituents
English
Subject two small
children Predicate chase
agent
theme Object that dog
Warlpiri
S
NP Aux V NP NP NP
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English and Warlpiri under Hypothesis 4
Functional structure represents gramamtical
relations and semantic roles
Constituent structure represents word order and
grouping of words into constituents
English
Subject two small
children Predicate chase
agent
theme Object that dog
Mapping from c-structure to f-structure
Warlpiri
S
NP Aux V NP NP NP
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English and Warlpiri under Hypothesis 4
Functional structure represents gramamtical
relations and semantic roles
Constituent structure represents word order and
grouping of words into constituents
English
Subject two small
children Predicate chase
agent
theme Object that dog
Mapping from c-structure to f-structure
Warlpiri
S
NP Aux V NP NP NP
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Keeping Score

• Hypothesis 3
• One structure contains a mish-mash of word order,
  constituency, grammatical relations, and thematic
  roles
• Adjunctions
• Empty categories and invisible constituents

• Hypothesis 4
• Need an extra data structure for grammatical
  relations and semantic roles
• Need a mapping between c-structure and
  f-structure
• Need a reproducible, falsifiable definition of
  grammatical relations.

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Levels of Representation in LFG
s np The bear vp ate np a sandwich
constituent structure
Grammatical encoding
SUBJ PRED OBJ
functional structure
Lexical mapping
Agent eat patient
thematic roles
Eat lt agent patient gt lexical
mapping SUBJ OBJ
Grammatical Encoding For English!!!
S
NP
SUBJ
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A surprise

• Syntax is not about the form (phrase structure)
  of sentences.
• It is about how strings of words are associated
  with their semantic roles.
• Phrase structure is only part of the solution.
• Sam saw Sue
• Sam perceiver
• Sue perceived

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Surprise (continued)

• Syntax is also about how to tell that two
  sentences are thematic paraphrases of each other
  (same phrases filling the same semantic roles).
• It seems that Sam ate the sandwich.
• It seems that the sandwich was eaten by Sam.
• Sam seems to have eaten the sandwich.
• The sandwich seems to have been eaten by Sam.

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How to associate phrases with their semantic
roles in LFG

• Starting from a constituent structure tree
• Grammatical encoding tells you how to find the
  subject.
• The bear is the subject.
• Lexical mapping tells you what semantic role the
  subject has.
• The subject is the agent.
• Therefore, the bear is the agent.

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Levels of Representation in LFG
s np The sandwich vp was eaten pp by the
bear constituent structure
Grammatical encoding
SUBJ PRED OBL
functional structure
Lexical mapping
patient eat
agent thematic roles
Eat lt agent patient gt lexical
mapping OBL SUBJ
Grammatical Encoding For English!!!
S
NP
SUBJ
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Active and Passive

• Active
• Patient is mapped to OBJ in lexical mapping.
• Passive
• Patient is mapped to SUBJ in lexical mapping.
• Notice that the grammatical encodings are the
  same for active and passive sentences!!!

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Passive mappings

• Starting from the constituent structure tree.
• The grammatical encoding tells you that the
  sandwich is the subject.
• The lexical mapping tells you that the subject is
  the patient.
• Therefore, the sandwich is the patient.
• The grammatical encoding tells you that the bear
  is oblique.
• The lexical mapping tells you that the oblique is
  the agent.
• Therefore, the bear is the agent.

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How you know that the active and passive have the
same meaning

• In both sentences, the mappings connect the bear
  to the agent role.
• In both sentences, the mappings connect the
  sandwich to the patient role (roll?)
• In both sentences, the verb is eat.

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Levels of Representation in LFG
s-bar np what s did np the bear
eat constituent structure
Grammatical encoding
OBJ SUBJ
PRED functional structure
Lexical mapping
patient agent
eat thematic roles
Eat lt agent patient gt lexical
mapping SUBJ OBJ
Grammatical Encoding For English!!!
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Wh-question

• Different grammatical encoding
• In this example, the OBJ is encoded as the NP
  immediately dominated by S-bar
• Same lexical mappings are used for
• What did the bear eat?
• The bear ate the sandwich.

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Functional Structure
SUBJ PRED bear
NUM sg PERS
3 DEF PRED
eatlt agent patient gt
SUBJ OBJ TENSE past OBJ
PRED sandwich
NUM sg PERS 3
DEF -

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Functional Structure

• Pairs of attributes (features) and values
• Attributes (in this example) SUBJ, PRED, OBJ,
  NUM, PERS, DEF, TENSE
• Values
• Atomic sg, past, , etc.
• Feature structure
• num sg, pred bear, def , person 3
• Semantic form eatltsubj obgt, bear, sandwich

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Semantic Forms

• Why are they values of a feature called PRED?
• In some approaches to semantics, even nouns like
  bear are predicates (function) that take one
  argument and returns true or false.
• Bear(x) is true when the variable x is bound to a
  bear.
• Bear(x) is false when x is not bound to a bear.

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Why is it called a Functional Structure?

• X squared
• 1
• 4
• 9
• 16
• 25

Each feature has a unique value.
Also, another term for grammtical relation is
grammatical function.
features
values
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We will use the terms functional structure,
f-structure and feature structure
interchangeably.
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Give a name to each function
f1
SUBJ PRED bear
NUM sg PERS
3 DEF PRED
eatlt agent patient gt
SUBJ OBJ TENSE past OBJ
PRED sandwich
NUM sg PERS 3
DEF -
f2

f3
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How to describe an f-structure

• F1(TENSE) past
• Function f1 applied to TENSE gives the value
  past.
• F1(SUBJ) PRED bear, NUM sg, PERS 3, DEF
• F2(NUM) sg

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Descriptions can be true or false

• F(a) v
• Is true if the feature-value pair a v is in f.
• Is false if the feature-value pair a v is not
  in f.

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This is the notation we really use

• (f1 TENSE) past
• Read it this way
• f1s tense is past.
• (f1 SUBJ) PRED bear, NUM sg, PERS 3, DEF
• (f2 NUM) sg

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Chains of function application

• (f1 SUBJ) f2
• (f2 NUM) sg
• ((f1 SUBJ) NUM) sg
• Write it this way.
• (f1 SUBJ NUM) sg
• Read it this way.
• f1s subjects number is sg.

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More f-descriptions

• (f a) v
• f is something that evaluates to a function.
• a is something that evaluates to an attribute.
• v is something that evaluates to a function,
  symbol, or semantic form.
• (f1 subj) (f1 xcomp subj)
• Used for matrix coding as subject. A subject is
  shared by the main clause and the complement
  clause (xcomp).
• (f1 (f6 case)) f6
• Used for obliques

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SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

S
NP VP
N V VP-bar
COMP VP
V PP
P NP
DET N
Lions seem to live in the forest
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SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f1
f2
S
n1
f3
NP VP
n4
n2
N V VP-bar
n5
n3
n6
f4
COMP VP
n7
n8
f5
f6
V PP
n10
n9
P NP
n12
n11
DET N
n13
n14
Lions seem to live in the forest
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SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f1
f2
S
n1
f3
NP VP
n4
n2
N V VP-bar
n5
n3
n6
f4
COMP VP
n7
n8
f5
f6
V PP
n10
n9
P NP
n12
n11
DET N
n13
n14
Lions seem to live in the forest