Grammatical Relations
and Lexical Functional Grammar
Grammar Formalisms
Spring Term 2004
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
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 verb’s
subcategorization list.
• Lexical Functional Grammar:
– Grammatical relations are labelled explicitly in a feature
structure.
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.
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)
Some differences between English and
Warlpiri (Australia)
S
VP’
NP
VP
Aux
The two small children
V
NP
are chasing that dog.
S
NP
Wita-jarra-rlu
Small-DU-ERG
AUX
V
NP
NP
NP
ka-pala
wajili-pi-nyi yalumpu kurdu-jarra-rlu maliki.
pres-3duSUBJ chase-NPAST that.ABS child-DU-ERG dog.ABS
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.
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.
Checking the hypotheses
• Hypothesis 2:
– Does it work for Warlpiri?
• Hypothesis 3:
– Does it work for Warlpiri?
English and Warlpiri Under Hypothesis 3
S
Deep structure
VP’
NP
VP
Aux
V
NP
English
S
Surface Structure
VP’
NP
VP
Aux
V
NP
English and Warlpiri under Hypothesis 3
S
VP’
VP
NP
Aux
Warlpiri
V
Deep structure
NP
S
NP
S
AUX S
S
NP
NP
S
Surface Structure
VP’
NP
VP
Aux
e
ee
V
NP
e
English and Warlpiri under Hypothesis 3
S
VP’
VP
NP
Aux
Warlpiri
V
S
NP
Deep structure
NP
Adjunctions: represent the
real word order
S
AUX S
S
NP
Remnants of the
original tree
represent
gramamtical
relations
NP
S
VP’
NP
VP
Aux
V
NP
e
ee
Empty
categories:
represent
semantic roles
Surface Structure
e
English and Warlpiri under Hypothesis 4
Constituent structure:
represents word order and
grouping of words into
constituents
English
S
Subject
VP’
NP
VP
Aux
Warlpiri
NP
V
V
NP
NP
NP
“two small
children”
Predicate
chase
agent
theme
Object
“that dog”
NP
S
Aux
Functional structure:
represents
grammatical relations
and semantic roles
English and Warlpiri under Hypothesis 4
Constituent structure:
represents word order and
grouping of words into
constituents
English
S
Subject
VP’
NP
VP
Aux
Warlpiri
NP
V
V
NP
chase
agent
theme
Object
“that dog”
NP
NP
NP
“two small
children”
Predicate
Mapping from c-structure to fstructure
S
Aux
Functional structure:
represents
gramamtical relations
and semantic roles
English and Warlpiri under Hypothesis 4
Constituent structure:
represents word order and
grouping of words into
constituents
English
S
Subject
VP’
NP
VP
Aux
V
NP
S
Aux
V
NP
NP
NP
“two small
children”
Predicate
chase
agent
theme
Object
“that dog”
NP
Mapping from c-structure
to f-structure
Warlpiri
Functional structure:
represents
gramamtical relations
and semantic roles
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.
Levels of Representation in
LFG
[s [np The bear] [vp ate [np a sandwich]]]
SUBJ
Agent
Eat < agent
SUBJ
PRED
SUBJ
OBJ
eat
functional structure
Lexical mapping
thematic roles
patient
patient >
lexical mapping
OBJ
S
NP
constituent structure
Grammatical encoding
VP
VP
V
NP
OBJ
V
PP
OBL
Grammatical
Encoding
For English!!!
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
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.
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.
Levels of Representation in
LFG
[s [np The sandwich ] [vp was eaten [pp by the bear]]]
constituent structure
Grammatical encoding
SUBJ
PRED
OBL
patient
eat
agent
Eat < agent
OBL
patient >
SUBJ
lexical mapping
SUBJ
S
NP
functional structure
Lexical mapping
thematic roles
VP
VP
V
NP
OBJ
V
PP
OBL
Grammatical
Encoding
For English!!!
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!!!
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.
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.
Levels of Representation in
LFG
[s-bar [np what ] [s did
[np the bear]
eat ]]
constituent structure
Grammatical encoding
OBJ
SUBJ
patient
Eat < agent
SUBJ
S-bar
NP
S
OBJ
agent
patient >
PRED
eat
functional structure
Lexical mapping
thematic roles
lexical mapping
OBJ
VP
S
NP
SUBJ
V
PP
OBL
Grammatical
Encoding
For English!!!
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.
Functional Structure
SUBJ
PRED
TENSE
OBJ
PRED ‘bear’
NUM
sg
PERS
3
DEF
+
‘eat< agent patient >
SUBJ OBJ
past
PRED ‘sandwich’
NUM sg
PERS 3
DEF
-
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: ‘eat<subj ob>’, ‘bear’, ‘sandwich’
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.
Why is it called a Functional
Structure?
X squared
1
1
2
4
3
9
Each feature has
a unique value.
Also, another term for
grammtical relation is
grammatical function.
4 16
5
features
25
values
We will use the terms functional structure,
f-structure and feature structure interchangeably.
Give a name to each function
f1
SUBJ
PRED ‘bear’
NUM
sg
f2
PERS
3
DEF
+
PRED
‘eat< agent patient >
SUBJ OBJ
TENSE
past
OBJ
PRED ‘sandwich’
NUM sg
f3 PERS 3
DEF
-
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
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.
This is the notation we really
use
• (f1 TENSE) = past
• Read it this way:
f1’s tense is past.
• (f1 SUBJ) = [PRED ‘bear’, NUM sg, PERS
3, DEF +]
• (f2 NUM) = sg
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.
“f1’s subject’s number is sg.”
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
SUBJ
PRED
TENSE
VFORM
XCOMP
S
NP
N
VP
V
PRED ‘lion’
NUM
pl
PERS
3
‘seem < theme > SUBJ’
XCOMP
pres
fin
SUBJ [ ]
VFORM INF
PRED ‘live< theme loc >’
VP-bar
SUBJ
OBL-loc
COMP VP
V
PP
P
NP
DET
N
Lions seem to live in the forest
CASE
PRED
OBJ
OBL-loc OBJ
OBL-loc
‘in<OBJ>’
PRED ‘forest’
NUM sg
PERS 3
DEF
+
SUBJ
f1
f2
PRED
TENSE
VFORM
XCOMP
S n1
n2
NP
n3
N
VP
V
n5
n4
VP-bar
SUBJ
n6
f4
n7
COMP VP
PRED ‘lion’
NUM
pl
PERS
3
‘seem < theme > SUBJ’
XCOMP
pres
fin
SUBJ [ ] f3
VFORM INF
PRED ‘live< theme loc >’
OBL-loc
n8
f5
V
PP
n9
P
n10
NP
n11
DET
N
n12
n13
n14
Lions seem to live in the forest
CASE
PRED
OBJ
f6
OBL-loc OBJ
OBL-loc
‘in<OBJ>’
PRED ‘forest’
NUM sg
PERS 3
DEF
+
SUBJ
f1
f2
PRED
TENSE
VFORM
XCOMP
S n1
n2
NP
n3
N
VP
V
n5
n4
VP-bar
SUBJ
n6
f4
n7
COMP VP
PRED ‘lion’
NUM
pl
PERS
3
‘seem < theme > SUBJ’
XCOMP
pres
fin
SUBJ [ ] f3
VFORM INF
PRED ‘live< theme loc >’
OBL-loc
n8
f5
V
PP
n9
P
n10
NP
n11
DET
N
n12
n13
n14
Lions seem to live in the forest
CASE
PRED
OBJ
f6
OBL-loc OBJ
OBL-loc
‘in<OBJ>’
PRED ‘forest’
NUM sg
PERS 3
DEF
+