Feature structures and unification

Attributes and values

The following object describes a class of persons:



age 22gender Mnationality Norwegian





Attributes




AttributesValues




Let this be the class of persons described:




Let this be the class of persons described:Then remove a feature...


age 22

nationality Norwegian


Let this be the class of persons described:Then remove a feature...


age 22



Let this be the class of persons described:Then remove a feature...and the class grows.


age 22



Let this be the class of persons described:Then remove a feature...and the class grows.Add a feature instead...


age 22gender Mnationality Norwegianeyecolour brown


Let this be the class of persons described:Then remove a feature...and the class grows.Add a feature instead...


age 22gender Mnationality Norwegianeyecolour brown


Let this be the class of persons described:Then remove a feature...and the class grows.Add a feature instead...and the class shrinks.



A grammar example:




A grammar example:

cat NPnumber sgperson 3




A grammar example:


This object describes a class of phrases:




A grammar example:


This object describes a class of phrases:


a manthe horsesome red carthe King’s manwaternice beer...



A grammar example:


This object describes a class of phrases:Remove a feature...





A grammar example:

cat NP

person 3

This object describes a class of phrases:Remove a feature...





A grammar example:

cat NP

person 3

This object describes a class of phrases:Remove a feature...and the class grows.



menthe horsessome red carsthe King’s menwatersnice beers...


f1:

Feature structures as functions


• A set of ordered pairs (of attributes and values)

f1:



• A set of ordered pairs (of attributes and values)• Never more than one occurrence of a given attribute

f1:



• 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:



• 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:




Example:

f1(cat)=NPf1(number)=sgf1(person)=3

f1:




Example:


Values can be atomic or complex:

f1:




Example:


Values can be atomic or complex:

f1:

agreement

cat NPnumber singularperson third


Subsumption

cat NP

Subsumption

cat NP

agreement

cat NP

number singular

Subsumption

cat NP

agreement

cat NP

number singular

agreement


Subsumption

cat NP

agreement

cat NP

number singular

agreement


agreement


subjectnumber singularperson third

Subsumption

cat NP

agreement

cat NP

number singular

agreement


agreement


subjectnumber singularperson third

agreement


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


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


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


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


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


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


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

cat NP

number singular

Unification

cat NP


=

cat NP

agreement

cat NP

number singular

Unification

agreement

cat NP

number singular

cat NP


=

cat NP

agreement

cat NP

number singular

Unification

agreement

cat NP

number singular

cat NP


=

cat NP

agreement

cat NP

number singular

agreement

cat NP

number singular

=

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

cat NP

number singular

Unification

agreement

cat NP

number singular

subject

=



subject agreement person third

agreement

cat NP

number singular

Unification

agreement

cat NP

number singular

subject

=



subject agreement person third

agreement

cat NP

number singular

subject


agreementnumber singular

person third

=

Unification

Unification

subject



Unification

subject


agreement

1

1

subject



Compare with:

Unification

subject


agreement

subject agreement

1

person third

1

subject



Unification

Compare with:

subject


agreement

subject agreement


person third=

1

person third

1

subject agreement 1

1

subject



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:


1 2 3=

Unification

subject

agreement

agreement

1

2f1:


1 2 3=

subject

agreement

agreementf1:

3

3

Unification

subject

agreement

agreement

1

2f1:


1 2 3=

subject

agreement

agreementf1:

3

3

agreement

subject agreementf1:

Unification

Unification through constraints:

subject

agreement

agreement

1

2f1:



subject

agreement

agreement

1

2f1:



Alternative notation with paths:

subject

agreement

agreement

1

2f1:




‹agreement› = ‹subject agreement›

This means that the two paths have the same (unspecified) value.

subject

agreement

agreement

1

2f1:






A constraint may also specify a value:

subject

agreement

agreement

1

2f1:







‹agreement number› = sg

subject

agreement

agreement

1

2f1:








We thus have two types of constraints:

subject

agreement

agreement

1

2f1:








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:


VP

S

NPsleepsJohn

Grammar:

S → NP VP

Lexicon:

John NPsleeps VPsleep VP

A one-rule grammar with lexicon:Phrase structure tree:


VP

S

NPsleepsJohn

Grammar:

S → NP VP


We incorporate features and unification to handle agreement.


Lexicon:


VP

S

NPsleepsJohn

Grammar:

S → NP VP



Grammar:

S -> NP VP ‹f:S› = ‹f:VP› ‹f:S subject› = ‹f:NP›


Lexicon:


VP

S

NPsleepsJohn

Grammar:

S → NP VP



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›


Lexicon:



The rule now describes this subtree:



1subject

2

2

NP VP1

S



1subject

2

2

NP VP1

The lexical entries:

S



1subject

2

2

NP VP1

The lexical entries:

agreement

John sleepsnumber singular

person thirdagreement

number singular

person thirdsubject

NP VP

S


1subject

2

2

NP VP1

agreement



number singular

person thirdsubject

NP VP

What happens if we insert ‘John’ as the NP daughter?

S


1subject

2

2

NP VP1

agreement



number singular

person thirdsubject

NP VP

S


1subject

2

S

2

NP VP1

John

sleeps


person thirdsubject

VP


person third


1subject

2

S

2

NP VP1

John

sleeps


person thirdsubject

VP


person third

'sleeps' can now only be inserted if itsagreement-features are compatible with 'John'.


1subject

2

S

2

NP VP1

John

sleeps


person thirdsubject

VP


person third


1subject

2

S

2

NP VP1

John sleeps


person third

Feature structures inLexical-Functional Grammar

1. [S I forced him [S PRO to be kind]]

Phrase structure analyses in traditional transformational grammar:


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:









2. [S I believed him [VP' to be kind]]











4. [S John tends [VP' to shout]]












6. [S John [VP' was killed]]















How does LFG capture













How does LFG capture•the difference between 1 and 2,













How does LFG capture•the difference between 1 and 2,•the non-argument status of the subject of 3 and 4,













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?













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


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


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


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


TENSE pret

OBJ




f1 f2

f5

f6



TENSE pret

OBJ





f1 f2

f5

f6

Linking

A verb form contains information about the way in whichsemantic arguments are linked to syntactic functions:

Linking


"reparerer": reparere<agent, theme>

SUBJ OBJ

Linking



SUBJ OBJ

"repareres": reparere<agent, theme>

SUBJ

Linking



SUBJ OBJ


SUBJ

”like": like<experiencer, theme>

SUBJ OBJ

Linking



SUBJ OBJ


SUBJ


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:


SUBJ OBJ


SUBJ


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":


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":


SUBJ

PRED

OBJ

ADJUNCT

"the boy"

”the bike"

{”in the garage"}

repair<SUBJ, OBJ>"


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"



SUBJ

PRED

OBJ

ADJUNCT

"the boy"

”the bike"

{”in the garage"}

repair<SUBJ, OBJ>"


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"



TENSE pret

OBJ





f1 f2

f5

f6

Describing parts of the structureby means of equations


TENSE pret

OBJ





f1 f2

f5

f6


f1 (TENSE) = pret


TENSE pret

OBJ





f1 f2

f5

f6


f1 (TENSE) = pretf1 (SUBJ) = f2


TENSE pret

OBJ





f1 f2

f5

f6


f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nom


TENSE pret

OBJ





f1 f2

f5

f6


f1 (TENSE) = pretf1 (SUBJ) = f2f2 (CASE) = nomf1 (SUBJ)(CASE) = nom


TENSE pret

OBJ





f1 f2

f5

f6



f2


TENSE pret

OBJ





f1 f2

f5

f6



f2

Alternative notation:

(f1 TENSE) = pret(f1 SUBJ) = f2(f2 CASE) = nom(f1 SUBJ CASE) = nom


TENSE pret

OBJ





f1 f2

f5

f6



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')


( SUBJ)

( OBJ)

( XCOMP)

VP

V NP

S

NPI

forced himVP'

to leave

S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP

V NP

S

NPI

forced himVP'

to leave

( SUBJ)

( OBJ)

( XCOMP)

S -> NP VP

VP -> V (NP) (VP')


( 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')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( SUBJ)

( OBJ)

( XCOMP)


Index the c-structure nodes

S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( OBJ)

( XCOMP)


(f1 SUBJ)

Instantiate the metavariables:Replace them with f-structurevariables based on the node indices.

S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( OBJ)

( XCOMP)


(f1 SUBJ)f2


S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( OBJ)

( XCOMP)


(f1 SUBJ)f2 f1


S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( OBJ)

( XCOMP)


(f1 SUBJ)f2 f1f3


S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( OBJ)

( XCOMP)


(f1 SUBJ)f2 f1f3

f3


S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( OBJ)

( XCOMP)


(f1 SUBJ)f2 f1f3

f3f4


S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( XCOMP)


(f1 SUBJ)f2 f1f3

f3f4 (f3 OBJ)


S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP:3

V:4 NP:5

S:1

NP:2I

forced himVP':6

to leave

( XCOMP)


(f1 SUBJ)f2 f1f3

f3f4 (f3 OBJ)f5


S -> NP VP

VP -> V (NP) (VP')


( 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)


S -> NP VP

VP -> V (NP) (VP')


( 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


S -> NP VP

VP -> V (NP) (VP')


( 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



S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'(f4 TENSE) = pret(f4 OBJ) = (f4 XCOMP SUBJ)

(f1 SUBJ)f2 f1f3


The tree has done its job:Forget it.

S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)


(f1 SUBJ)f2f1f3f3f4(f3 OBJ)f5(f3 XCOMP)f6

Collect the instantiated equationsinto an f-description



Solve the equations in any orderto constuct an f-structure



SUBJ


f1f2



SUBJ


f1f2

f3



SUBJ


f1f2

f3

f4



SUBJ

OBJ


f1f2

f5

f3

f4



SUBJ

OBJ


f1f2

f3

f4

f5



SUBJ

OBJ

XCOMP


f1f2

f6

f3

f4

f5



SUBJ

OBJ

XCOMP

PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›'


f1f2

f6

f3

f4

f5



SUBJ

TENSE pret

OBJ

XCOMP



f1f2

f6

f3

f4

f5



SUBJ

TENSE pret

OBJ

XCOMP SUBJ



f1f2

f6

f3

f4

f5



SUBJ

TENSE pret

OBJ

XCOMP SUBJ



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


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



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



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


f1f2

f6

f3

f4

f5

S -> NP VP

VP -> V (NP) (VP')


( SUBJ)

( OBJ)

( XCOMP)

VP

V NP

S

NPI

forced himVP'

to leave

( SUBJ)

( OBJ)

( XCOMP)


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


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


SUBJ

TENSE pret

OBJ

XCOMP SUBJ

PRED ’BELIEVE‹(f4 SUBJ)(f4 XCOMP)›(f4 OBJ)'

f1f2

f6

f3

f4

f5


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







This enables us to derive:

gutten har løptgutten måtte løpe







This enables us to derive:

gutten har løptgutten måtte løpe

But does it exclude the following?

*gutten har løpe*gutten måtte løpt


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



Feature structures and unification

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