Post on 05-Jan-2016
description
Feature structures and unification
Attributes and values
The following object describes a class of persons:
Attributes and values
The following object describes a class of persons:
age 22gender Mnationality Norwegian
Attributes and values
The following object describes a class of persons:
age 22gender Mnationality Norwegian
Attributes and values
Attributes
The following object describes a class of persons:
age 22gender Mnationality Norwegian
Attributes and values
AttributesValues
The following object describes a class of persons:
age 22gender Mnationality Norwegian
Attributes and values
Let this be the class of persons described:
The following object describes a class of persons:
age 22gender Mnationality Norwegian
Attributes and values
Let this be the class of persons described:
The following object describes a class of persons:
age 22gender Mnationality Norwegian
Attributes and values
Let this be the class of persons described:Then remove a feature...
The following object describes a class of persons:
age 22
nationality Norwegian
Attributes and values
Let this be the class of persons described:Then remove a feature...
The following object describes a class of persons:
age 22
nationality Norwegian
Attributes and values
Let this be the class of persons described:Then remove a feature...and the class grows.
The following object describes a class of persons:
age 22
nationality Norwegian
Attributes and values
Let this be the class of persons described:Then remove a feature...and the class grows.Add a feature instead...
The following object describes a class of persons:
age 22gender Mnationality Norwegianeyecolour brown
Attributes and values
Let this be the class of persons described:Then remove a feature...and the class grows.Add a feature instead...
The following object describes a class of persons:
age 22gender Mnationality Norwegianeyecolour brown
Attributes and values
Let this be the class of persons described:Then remove a feature...and the class grows.Add a feature instead...and the class shrinks.
The following object describes a class of persons:
age 22gender Mnationality Norwegian
A grammar example:
Attributes and values
The following object describes a class of persons:
age 22gender Mnationality Norwegian
A grammar example:
cat NPnumber sgperson 3
Attributes and values
The following object describes a class of persons:
age 22gender Mnationality Norwegian
A grammar example:
cat NPnumber sgperson 3
This object describes a class of phrases:
Attributes and values
The following object describes a class of persons:
age 22gender Mnationality Norwegian
A grammar example:
cat NPnumber sgperson 3
This object describes a class of phrases:
Attributes and values
a manthe horsesome red carthe King’s manwaternice beer...
The following object describes a class of persons:
age 22gender Mnationality Norwegian
A grammar example:
cat NPnumber sgperson 3
This object describes a class of phrases:Remove a feature...
Attributes and values
a manthe horsesome red carthe King’s manwaternice beer...
The following object describes a class of persons:
age 22gender Mnationality Norwegian
A grammar example:
cat NP
person 3
This object describes a class of phrases:Remove a feature...
Attributes and values
a manthe horsesome red carthe King’s manwaternice beer...
The following object describes a class of persons:
age 22gender Mnationality Norwegian
A grammar example:
cat NP
person 3
This object describes a class of phrases:Remove a feature...and the class grows.
Attributes and values
a manthe horsesome red carthe King’s manwaternice beer...
menthe horsessome red carsthe King’s menwatersnice beers...
cat NPnumber sgperson 3
f1:
Feature structures as functions
cat NPnumber sgperson 3
• A set of ordered pairs (of attributes and values)
f1:
Feature structures as functions
cat NPnumber sgperson 3
• A set of ordered pairs (of attributes and values)• Never more than one occurrence of a given attribute
f1:
Feature structures as functions
cat NPnumber sgperson 3
• A set of ordered pairs (of attributes and values)• Never more than one occurrence of a given attribute• Never more than one value of a given attribute (but different attributes can have the same value)
f1:
Feature structures as functions
cat NPnumber sgperson 3
• A set of ordered pairs (of attributes and values)• Never more than one occurrence of a given attribute• Never more than one value of a given attribute (but different attributes can have the same value)• Hence such a structure can be considered as a function from attributes to values
f1:
Feature structures as functions
cat NPnumber sgperson 3
• A set of ordered pairs (of attributes and values)• Never more than one occurrence of a given attribute• Never more than one value of a given attribute (but different attributes can have the same value)• Hence such a structure can be considered as a function from attributes to values
Example:
f1(cat)=NPf1(number)=sgf1(person)=3
f1:
Feature structures as functions
cat NPnumber sgperson 3
• A set of ordered pairs (of attributes and values)• Never more than one occurrence of a given attribute• Never more than one value of a given attribute (but different attributes can have the same value)• Hence such a structure can be considered as a function from attributes to values
Example:
f1(cat)=NPf1(number)=sgf1(person)=3
Values can be atomic or complex:
f1:
Feature structures as functions
cat NPnumber sgperson 3
• A set of ordered pairs (of attributes and values)• Never more than one occurrence of a given attribute• Never more than one value of a given attribute (but different attributes can have the same value)• Hence such a structure can be considered as a function from attributes to values
Example:
f1(cat)=NPf1(number)=sgf1(person)=3
Values can be atomic or complex:
f1:
agreement
cat NPnumber singularperson third
Feature structures as functions
Subsumption
Subsumption
cat NP
Subsumption
cat NP
agreement
cat NP
number singular
Subsumption
cat NP
agreement
cat NP
number singular
agreement
cat NPnumber singularperson third
Subsumption
cat NP
agreement
cat NP
number singular
agreement
cat NPnumber singularperson third
agreement
cat NPnumber singularperson third
subjectnumber singularperson third
Subsumption
cat NP
agreement
cat NP
number singular
agreement
cat NPnumber singularperson third
agreement
cat NPnumber singularperson third
subjectnumber singularperson third
agreement
cat NPnumber singularperson third
subject
1
1
Subsumption
Not subsumption
agreement
cat NP
number singular1
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
1
2
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
1
2
1 2, 2 1
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
1
2
3
1 2, 2 1
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
1
2
3
1 2, 2 1
1 3, 3 1
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
agreement
cat NPnumber singularperson third
1
2
3
4
1 2, 2 1
1 3, 3 1
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
agreement
cat NPnumber singularperson third
1
2
3
4
1 2, 2 1
1 3, 3 1
1 4
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
agreement
cat NPnumber singularperson third
1
2
3
4
1 2, 2 1
1 3, 3 1
1 4
2 4
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
agreement
cat NPnumber singularperson third
1
2
3
4
1 2, 2 1
1 3, 3 1
1 4
2 4
1 2 = 4
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
agreement
cat NPnumber singularperson third
1
2
3
4
1 2, 2 1
1 3, 3 1
1 4
2 4
1 2 = 4
1 3 = fail
Not subsumption
agreement
cat NP
number singular
agreement
cat NP
person third
agreement
cat NP
number plural
agreement
cat NPnumber singularperson third
1
2
3
4
1 2, 2 1
1 3, 3 1
1 4
2 4
1 2 = 4
1 3 = fail
Unification:a b = cif and only ifa c andb c andthere is no d such thata d andb d andd c
Not subsumption
Unification
cat NP
Unification
cat NP
agreement number singular
Unification
cat NP
agreement number singular
=agreement
cat NP
number singular
Unification
cat NP
agreement number singular
=
cat NP
agreement
cat NP
number singular
Unification
agreement
cat NP
number singular
cat NP
agreement number singular
=
cat NP
agreement
cat NP
number singular
Unification
agreement
cat NP
number singular
cat NP
agreement number singular
=
cat NP
agreement
cat NP
number singular
agreement
cat NP
number singular
=
Unification
Unification
Unification
agreement
cat NP
number singular
Unification
agreement
cat NP
number singular
=agreement
cat NP
number singular
Unification
agreement
cat NP
number singular
subject
=
agreement number singular
agreement number singular
agreement
cat NP
number singular
Unification
agreement
cat NP
number singular
subject
=
agreement number singular
agreement number singular
subject agreement person third
agreement
cat NP
number singular
Unification
agreement
cat NP
number singular
subject
=
agreement number singular
agreement number singular
subject agreement person third
agreement
cat NP
number singular
subject
agreement number singular
agreementnumber singular
person third
=
Unification
Unification
subject
agreement number singular
agreement number singular
Unification
subject
agreement number singular
agreement
1
1
subject
agreement number singular
agreement number singular
Compare with:
Unification
subject
agreement number singular
agreement
subject agreement
1
person third
1
subject
agreement number singular
agreement number singular
Unification
Compare with:
subject
agreement number singular
agreement
subject agreement
agreementnumber singular
person third=
1
person third
1
subject agreement 1
1
subject
agreement number singular
agreement number singular
Unification
Compare with:
Unification
subject
agreement
agreement
1
2f1:
Unification
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
1 2 3=
Unification
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
1 2 3=
subject
agreement
agreementf1:
3
3
Unification
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
1 2 3=
subject
agreement
agreementf1:
3
3
agreement
subject agreementf1:
Unification
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
1 2 3=
subject
agreement
agreementf1:
3
3
agreement
subject agreementf1:
Unification
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
1 2 3=
subject
agreement
agreementf1:
3
3
agreement
subject agreementf1:
Unification
Unification through constraints:
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification through constraints:
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification through constraints:
Alternative notation with paths:
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification through constraints:
Alternative notation with paths:
‹agreement› = ‹subject agreement›
This means that the two paths have the same (unspecified) value.
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification through constraints:
Alternative notation with paths:
‹agreement› = ‹subject agreement›
This means that the two paths have the same (unspecified) value.
A constraint may also specify a value:
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification through constraints:
Alternative notation with paths:
‹agreement› = ‹subject agreement›
This means that the two paths have the same (unspecified) value.
A constraint may also specify a value:
‹agreement number› = sg
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification through constraints:
Alternative notation with paths:
‹agreement› = ‹subject agreement›
This means that the two paths have the same (unspecified) value.
A constraint may also specify a value:
‹agreement number› = sg
We thus have two types of constraints:
subject
agreement
agreement
1
2f1:
f1(agreement) = f1(subject)(agreement)
Unification through constraints:
Alternative notation with paths:
‹agreement› = ‹subject agreement›
This means that the two paths have the same (unspecified) value.
A constraint may also specify a value:
‹agreement number› = sg
We thus have two types of constraints:
‹attribute path› = Atomic value (The path has the specified value)‹attribute path› = ‹attribute path› (The two paths have the same value)
Incorporating unification in a phrase structure grammar
VP
S
NPsleepsJohn
Phrase structure tree:
Incorporating unification in a phrase structure grammar
VP
S
NPsleepsJohn
Grammar:
S → NP VP
Lexicon:
John NPsleeps VPsleep VP
A one-rule grammar with lexicon:Phrase structure tree:
Incorporating unification in a phrase structure grammar
VP
S
NPsleepsJohn
Grammar:
S → NP VP
A one-rule grammar with lexicon:Phrase structure tree:
We incorporate features and unification to handle agreement.
Incorporating unification in a phrase structure grammar
Lexicon:
John NPsleeps VPsleep VP
VP
S
NPsleepsJohn
Grammar:
S → NP VP
A one-rule grammar with lexicon:Phrase structure tree:
We incorporate features and unification to handle agreement.
Grammar:
S -> NP VP ‹f:S› = ‹f:VP› ‹f:S subject› = ‹f:NP›
Incorporating unification in a phrase structure grammar
Lexicon:
John NPsleeps VPsleep VP
VP
S
NPsleepsJohn
Grammar:
S → NP VP
A one-rule grammar with lexicon:Phrase structure tree:
We incorporate features and unification to handle agreement.
Lexicon:
John NP ‹f:NP agreement number› = singular ‹f:NP agreement person› = third
sleeps VP ‹f:VP subject agreement number› = singular ‹f:VP subject agreement person› = third
sleep VP ‹f:VP subject agreement number› = plural
Grammar:
S -> NP VP ‹f:S› = ‹f:VP› ‹f:S subject› = ‹f:NP›
Incorporating unification in a phrase structure grammar
Lexicon:
John NPsleeps VPsleep VP
Incorporating unification in a phrase structure grammar
The rule now describes this subtree:
Incorporating unification in a phrase structure grammar
The rule now describes this subtree:
1subject
2
2
NP VP1
S
Incorporating unification in a phrase structure grammar
The rule now describes this subtree:
1subject
2
2
NP VP1
The lexical entries:
S
Incorporating unification in a phrase structure grammar
The rule now describes this subtree:
1subject
2
2
NP VP1
The lexical entries:
agreement
John sleepsnumber singular
person thirdagreement
number singular
person thirdsubject
NP VP
S
Incorporating unification in a phrase structure grammar
1subject
2
2
NP VP1
agreement
John sleepsnumber singular
person thirdagreement
number singular
person thirdsubject
NP VP
What happens if we insert ‘John’ as the NP daughter?
S
Incorporating unification in a phrase structure grammar
1subject
2
2
NP VP1
agreement
John sleepsnumber singular
person thirdagreement
number singular
person thirdsubject
NP VP
S
Incorporating unification in a phrase structure grammar
1subject
2
2
NP VP1
agreement
John sleepsnumber singular
person thirdagreement
number singular
person thirdsubject
NP VP
S
Incorporating unification in a phrase structure grammar
1subject
2
S
2
NP VP1
John
sleeps
agreementnumber singular
person thirdsubject
VP
agreementnumber singular
person third
Incorporating unification in a phrase structure grammar
1subject
2
S
2
NP VP1
John
sleeps
agreementnumber singular
person thirdsubject
VP
agreementnumber singular
person third
'sleeps' can now only be inserted if itsagreement-features are compatible with 'John'.
Incorporating unification in a phrase structure grammar
1subject
2
S
2
NP VP1
John
sleeps
agreementnumber singular
person thirdsubject
VP
agreementnumber singular
person third
Incorporating unification in a phrase structure grammar
1subject
2
S
2
NP VP1
John
sleeps
agreementnumber singular
person thirdsubject
VP
agreementnumber singular
person third
Incorporating unification in a phrase structure grammar
1subject
2
S
2
NP VP1
John sleeps
agreementnumber singular
person third
Feature structures inLexical-Functional Grammar
1. [S I forced him [S PRO to be kind]]
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
4. [S John tends [VP' to shout]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
4. [S John tends [VP' to shout]]
6. [S John [VP' was killed]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
4. [S John tends [VP' to shout]]
6. [S John [VP' was killed]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
How does LFG capture
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
4. [S John tends [VP' to shout]]
6. [S John [VP' was killed]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
How does LFG capture•the difference between 1 and 2,
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
4. [S John tends [VP' to shout]]
6. [S John [VP' was killed]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
How does LFG capture•the difference between 1 and 2,•the non-argument status of the subject of 3 and 4,
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
4. [S John tends [VP' to shout]]
6. [S John [VP' was killed]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
How does LFG capture•the difference between 1 and 2,•the non-argument status of the subject of 3 and4,•and the semantic role of the subject of 6?
1. [S I forced him [S PRO to be kind]]
2. [S I believed [S him to be kind]]
3. [S NP seems [S John to shout]]
4. [S NP tends [S John to shout]]
5. [S Bill [VP killed John]]
6. [S NP [VP was killed John]]
1. [S I forced him [VP' to be kind]]
2. [S I believed him [VP' to be kind]]
4. [S John tends [VP' to shout]]
6. [S John [VP' was killed]]
Phrase structure analyses in Lexical Functional Grammar:
Phrase structure analyses in traditional transformational grammar:
How does LFG capture•the difference between 1 and 2,•the non-argument status of the subject of 3 and 4,•and the semantic role of the subject of 6?
Answer: Don’t operate on the trees,but annotate them with relevant informationabout syntactic functions and semantic arguments.
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
AP
to
V
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
AP
to
VP
V NP
S
NP
I
believed
kindbe
him
VP'
TO VP
V AP
to V
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
V AP
to
VP
V NP
S
NP
I
believed
kindbe
him
VP'
TO VP
V AP
to
VP
V
S
NP
John
tends
shout
VP'
TO VP
V
to
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
V AP
to
VP
V NP
S
NP
I
believed
kindbe
him
VP'
TO VP
V AP
to
VP
V
S
NP
John
tends
shout
VP'
TO VP
V
to
VP
V
S
NP
John
was
Bill
VP
V PP
NP
killed
by P
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
V AP
to
VP
V NP
S
NP
I
believed
kindbe
him
VP'
TO VP
V AP
to
VP
V
S
NP
John
tends
shout
VP'
TO VP
V
to
VP
V
S
NP
John
was
Bill
VP
V PP
NP
killed
by P
INF
’FORCE ‹SUBJ OBJ XCOMP›’PRET
XCOMPOBJ
SUBJ
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
V AP
to
VP
V NP
S
NP
I
believed
kindbe
him
VP'
TO VP
V AP
to
VP
V
S
NP
John
tends
shout
VP'
TO VP
V
to
VP
V
S
NP
John
was
Bill
VP
V PP
NP
killed
by P
INFINF
XCOMPOBJ
SUBJ
’FORCE ‹SUBJ OBJ XCOMP›’PRET
XCOMPOBJ
SUBJ
PRETBELIEVE ‹SUBJ XCOMP› OBJ’
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
V AP
to
VP
V NP
S
NP
I
believed
kindbe
him
VP'
TO VP
V AP
to
VP
V
S
NP
John
tends
shout
VP'
TO VP
V
to
VP
V
S
NP
John
was
Bill
VP
V PP
NP
killed
by P
PRES
SUBJINF
INF
XCOMP
INF
XCOMPOBJ
SUBJ
’FORCE ‹SUBJ OBJ XCOMP›’PRET
XCOMPOBJ
SUBJ
TEND ‹XCOMP› SUBJ’
PRETBELIEVE ‹SUBJ XCOMP› OBJ’
VP
V NP
S
NP
I
forced
kindbe
him
VP'
TO VP
V AP
to
VP
V NP
S
NP
I
believed
kindbe
him
VP'
TO VP
V AP
to
VP
V
S
NP
John
tends
shout
VP'
TO VP
V
to
VP
V
S
NP
John
was
Bill
VP
V PP
NP
killed
by P
PRES
SUBJINF
INF
OBLag
XCOMP
INF
SUBJ
XCOMPOBJ
SUBJ
’FORCE ‹SUBJ OBJ XCOMP›’PRET
XCOMPOBJ
SUBJ
TEND ‹XCOMP› SUBJ’
PRET
KILL ‹OBLag SUBJ›’
BELIEVE ‹SUBJ XCOMP› OBJ’
The functional information in the annotations
is represented in a separate functional structure
(f-structure), in the form of an attribute-value graph:
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
F-structure for I forced him to leave
f1 f2
f5
f6
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Linking
A verb form contains information about the way in whichsemantic arguments are linked to syntactic functions:
Linking
A verb form contains information about the way in whichsemantic arguments are linked to syntactic functions:
"reparerer": reparere<agent, theme>
SUBJ OBJ
Linking
A verb form contains information about the way in whichsemantic arguments are linked to syntactic functions:
"reparerer": reparere<agent, theme>
SUBJ OBJ
"repareres": reparere<agent, theme>
SUBJ
Linking
A verb form contains information about the way in whichsemantic arguments are linked to syntactic functions:
"reparerer": reparere<agent, theme>
SUBJ OBJ
"repareres": reparere<agent, theme>
SUBJ
”like": like<experiencer, theme>
SUBJ OBJ
Linking
A verb form contains information about the way in whichsemantic arguments are linked to syntactic functions:
"reparerer": reparere<agent, theme>
SUBJ OBJ
"repareres": reparere<agent, theme>
SUBJ
”like": like<experiencer, theme>
SUBJ OBJ
”behage": behage<experiencer, theme>
OBJ SUBJ
Linking
If we assume a universal hierarchy of semantic roles and let the order ofthe arguments reflect the hierarchy, we don’t need to name the semantic roles:
"reparerer": reparere<agent, theme>
SUBJ OBJ
"repareres": reparere<agent, theme>
SUBJ
”like": like<experiencer, theme>
SUBJ OBJ
”behage": behage<experiencer, theme>
OBJ SUBJ
Linking
If we assume a universal hierarchy of semantic roles and let the order ofthe arguments reflect the hierarchy, we don’t need to name the semantic roles:
"reparerer": reparere<SUBJ, OBJ>
"repareres": reparere< , SUBJ>
”like": like< SUBJ, OBJ >
”behage": behage< OBJ, SUBJ >
Wellformedness constraints on functional structures:
SUBJ
PRED
OBJ
ADJUNCT
"the boy"
”the bike"
{”in the garage"}
repair<SUBJ, OBJ>"
”The boy repairs the bike in the garage":
Wellformedness constraints on functional structures:
SUBJ
PRED
OBJ
ADJUNCT
"the boy"
”the bike"
{”in the garage"}
repair<SUBJ, OBJ>"
1. Completeness: An f-structure must contain all grammaticalrelations mentioned in PRED’s subcategorization frame.
SUBJ
PRED
”the boy"
”use<SUBJ, OBJ>"
*”The boy uses":”The boy repairs the bike in the garage":
Wellformedness constraints on functional structures:
SUBJ
PRED
OBJ
ADJUNCT
"the boy"
”the bike"
{”in the garage"}
repair<SUBJ, OBJ>"
1. Completeness: An f-structure must contain all grammaticalrelations mentioned in PRED’s subcategorization frame.
2. Coherence: An f-structure cannot contain any subcategorizablegrammatical relations not mentioned in PRED’s subcategorization frame.
SUBJ
PRED
"gutten"
"sove<SUBJ>"
*"Gutten sover sykkelen":
OBJ "sykkelen"
”The boy repairs the bike in the garage":
Wellformedness constraints on functional structures:
SUBJ
PRED
OBJ
ADJUNCT
"the boy"
”the bike"
{”in the garage"}
repair<SUBJ, OBJ>"
1. Completeness: An f-structure must contain all grammaticalrelations mentioned in PRED’s subcategorization frame.
2. Coherence: An f-structure cannot contain any subcategorizablegrammatical relations not mentioned in PRED’s subcategorization frame.
3. Uniqueness: No grammatical relation (or other attribute) may occurmore than once in a functional structure.
SUBJ
PRED
”the boy"
”use<SUBJ, OBJ>"
*”The boy uses the bike the car ”:
OBJ "the bike"
OBJ ”the car"
”The boy repairs the bike in the garage":
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pret
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pretf1 (SUBJ) = f2
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nom
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nomf1 (SUBJ)(CASE) = nom
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nomf1 (SUBJ)(CASE) = nom
f2
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nomf1 (SUBJ)(CASE) = nom
f2
Alternative notation:
(f1 TENSE) = pret(f1 SUBJ) = f2(f2 CASE) = nom(f1 SUBJ CASE) = nom
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nomf1 (SUBJ)(CASE) = nom
f2
Alternative notation:
(f1 TENSE) = pret(f1 SUBJ) = f2(f2 CASE) = nom(f1 SUBJ CASE) = nom
(f1 OBJ) = (f1 XCOMP SUBJ)
SUBJPRED ’I’CASE nom
TENSE pret
OBJ
PRED ’HE’CASE oblNUM sg
XCOMPSUBJPRED ’LEAVE‹ SUBJ › ’
PRED ’FORCE‹ SUBJ OBJ XCOMP ›’
F-structure for I forced him to leave
f1 f2
f5
f6
Describing parts of the structureby means of equations
f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nomf1 (SUBJ)(CASE) = nom
f2
Alternative notation:
(f1 TENSE) = pret(f1 SUBJ) = f2(f2 CASE) = nom(f1 SUBJ CASE) = nom
(f1 OBJ) = (f1 XCOMP SUBJ)
How to incorporatef-structure information
into a grammar
S -> NP VP
VP -> V (NP) (VP')
S -> NP VP
VP -> V (NP) (VP')
( SUBJ)
( OBJ)
( XCOMP)
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP
V NP
S
NPI
forced himVP'
to leave
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( SUBJ)
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
Index the c-structure nodes
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3f4
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3f4 (f3 OBJ)
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3f4 (f3 OBJ)f5
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3f4 (f3 OBJ)f5 (f3 XCOMP)
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3f4 (f3 OBJ)f5 (f3 XCOMP)f6
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP:3
V:4 NP:5
S:1
NP:2I
forced himVP':6
to leave(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3f4 (f3 OBJ)f5 (f3 XCOMP)f6
Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2 f1f3
f3f4 (f3 OBJ)f5 (f3 XCOMP)f6
The tree has done its job:Forget it.
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
Collect the instantiated equationsinto an f-description
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
Solve the equations in any orderto constuct an f-structure
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
F-structure for I forced him to leave
Solve the equations in any orderto constuct an f-structure
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
F-structure for I forced him to leave
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
F-structure for I forced him to leave
f1f2
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
F-structure for I forced him to leave
f1f2
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
F-structure for I forced him to leave
f1f2
f3
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
F-structure for I forced him to leave
f1f2
f3
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
F-structure for I forced him to leave
f1f2
f3
f4
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
F-structure for I forced him to leave
f1f2
f3
f4
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
F-structure for I forced him to leave
f1f2
f5
f3
f4
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
F-structure for I forced him to leave
f1f2
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
XCOMP
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
XCOMP
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
XCOMP
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
XCOMP
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
XCOMP
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
XCOMP
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
OBJ
XCOMP
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
TENSE pret
OBJ
XCOMP
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
TENSE pret
OBJ
XCOMP
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)
(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
F-structure for I forced him to leave
f1f2
f6
f3
f4
f5
Notice: The f-structure hasfewer levels than the c-structurebecause of the nodes annotatedwith =↓
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
The relation is called a projection relation.
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
The nodes in the tree and the elements of the f-structurenow stand in a many-to-one relation:
f1f2
f6
f3
f4
f5
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
The relation is called a projection relation.A set of nodes which project the same f-structureare said to constitute a functional domain.
A functional domain
Let us now move from
I forced him to leave
to
I believed him to leave
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
f1f2
f6
f3
f4
f5
S -> NP VP
VP -> V (NP) (VP')
forced: ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP
V NP
S
NPI
forced himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
All we need to change is the lexical entry:
S -> NP VP
VP -> V (NP) (VP')
believed: ( PRED) = ’BELIEVE‹( SUBJ) ( XCOMP)›( OBJ)'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
( SUBJ)
( OBJ)
( XCOMP)
VP
V NP
S
NPI
believed himVP'
to leave
( SUBJ)
( OBJ)
( XCOMP)
( PRED) = ’BELIEVE‹( SUBJ) ( XCOMP)›( OBJ)'( TENSE) = pret( OBJ) = ( XCOMP SUBJ)
All we need to change is the lexical entry:
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'
f1f2
f6
f3
f4
f5
This leads to the following change in the f-structure:
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED ’BELIEVE‹(f4 SUBJ)(f4 XCOMP)›(f4 OBJ)'
f1f2
f6
f3
f4
f5
This leads to the following change in the f-structure:
SUBJ
TENSE pret
OBJ
XCOMP SUBJ
PRED ’BELIEVE‹(f4 SUBJ)(f4 XCOMP)›(f4 OBJ)'
f1f2
f6
f3
f4
f5
This leads to the following change in the f-structure:
The only change is in the mapping between syntactic functionsand argument positions, as expressed in the value of PRED.The syntax as such is unchanged.
Constraint Equations
Consider these lexical entries:
ha V (↑PRED)='ha<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP PTC)=perf
måtte V (↑PRED)='måtte<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP VFORM)=inf
løpe V (↑PRED)='løpe<(↑ SUBJ)>' (↑ VFORM)=inf
løpt V (↑PRED)='løpe<(↑ SUBJ)>' (↑ PTC)=perf
Constraint Equations
Consider these lexical entries:
ha V (↑PRED)='ha<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP PTC)=perf
måtte V (↑PRED)='måtte<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP VFORM)=inf
løpe V (↑PRED)='løpe<(↑ SUBJ)>' (↑ VFORM)=inf
løpt V (↑PRED)='løpe<(↑ SUBJ)>' (↑ PTC)=perf
This enables us to derive:
gutten har løptgutten måtte løpe
Constraint Equations
Consider these lexical entries:
ha V (↑PRED)='ha<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP PTC)=perf
måtte V (↑PRED)='måtte<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP VFORM)=inf
løpe V (↑PRED)='løpe<(↑ SUBJ)>' (↑ VFORM)=inf
løpt V (↑PRED)='løpe<(↑ SUBJ)>' (↑ PTC)=perf
This enables us to derive:
gutten har løptgutten måtte løpe
But does it exclude the following?
*gutten har løpe*gutten måtte løpt
Constraint Equations
We need to change some equations into constraint equations:
ha V (↑PRED)='ha<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP PTC)=c perf
måtte V (↑PRED)='måtte<(↑ SUBJ)(↑ XCOMP)>' (↑ XCOMP VFORM)=c inf
løpe V (↑PRED)='løpe<(↑ SUBJ)>' (↑ VFORM)=inf
løpt V (↑PRED)='løpe<(↑ SUBJ)>' (↑ PTC)=perf