Context-Free Parsing

Part 2

Features and Unification

2/21

Parsing with features

• We need to constrain the rules in CFGs, for example– to coerce agreement within and between constituents– to pass features around– to enforce subcategorisation constraints

• Features can be easily added to our grammars• And later we’ll see that feature bundles can

completely replace constituents

3/21

Parsing with features

• Rules can stipulate values, or placeholders (variables) for values

• Features can be used within the rule, or passed up via the mother nodes

• Example: subject-verb agreement

S NP VP [if NP and VP agree in number] number of NP depends on noun and/or determiner number of VP depends on verb

S NP(num=X) VP (num=X)

NP (num=X) det(num=X) n (num=X)

VP(num=X) v(num=X) NP(num=?)

4/21

Declarative nature of featuresThe rules can be used in

various ways– To build an NP only if det and n agree

(bottom-up)– When generating an NP, to choose an

n which agrees with the det (if working L-to-R) (top-down)

– To show that the num value for an NP comes from its components (percolation)

– To ensure that the num value is correctly set when generating an NP (inheritance)

– To block ill-formed input

NP (num=X) det(num=X) n (num=X)

this det (num=sg)

these det (num=pl)

the det (num=?)

man n (num=sg)

men n (num=pl)

det(num=sg) n(num=sg)

this man

NP (num=sg)

n(num=pl)

men

5/21

Use of variables• Unbound

(unassigned) variables (ie variables with a free value):– the can combine with

any value for num– Unification means that

the num value for the is set to sg

NP (num=X) det(num=X) n (num=X)

this det (num=sg)

these det (num=pl)

the det (num=?)

man n (num=sg)

men n (num=pl)

det(num=?) n(num=sg)

the man

NP (num=sg)

6/21

Parsing with features• Features must be compatible• Formalism should allow features to remain

unspecified• Feature mismatch can be used to block false

analyses, and disambiguate– e.g. they can fish ~ he can fish ~ he cans fish

• Formalism may have attribute-value pairs, or rely on argument positione.g. NP(_num,_sem) det(_num) n (_num,_sem) an = det(sing) the = det(_num) man = n(sing,hum)

7/21

Parsing with features

• Using features to impose subcategorization constraints

VP v e.g. dance

VP v NP e.g. eat

VP v NP NP e.g. give

VP v PP e.g. wait (for)

VP(_num) v(_num,intr)

VP(_num) v(_num,trans) NP

VP(_num) v(_num,ditrans) NP NP

VP(_num) v(_num,prepobj(_case)) PP(_case)

PP(_case) prep(_case) NP

dance = v(plur,intr)

dances = v(sing,intr)

danced = v(_num,intr)

waits = v(sing,prepobj(for))

for = prep(for)

8/21

v(sing,intrans)

S NP(_num) VP(_num)NP(_num) det(_num) n(_num)VP(_num) v(_num,intrans)VP(_num) v (_num,trans) NP(_1)

Parsing with features (top-down)

S NP(_num) VP(_num)S

NP VP(_num) (_num)

NP(_num) det(_num) n(_num)

the man shot those elephants

det n(_num) (_num)

the = det(_num)

the

man = n(sing)

man

VP(sing) v(sing,intrans)

shot = v(sing,trans)

(sing)

(sing)(sing)

(sing)VP(sing) v(sing,trans) NP(_1)

shot = v(sing,trans)

v NP(sing,trans) (_1)

shot det n (_1) (_1)

those elephants

(pl)

(pl)

NP(_1) det(_1) n(_1)

those = det(pl)

elephants = n(pl)

_num=sing

(pl)

9/21

S NP(_num) VP(_num)NP(_num) det(_num) n(_num)VP(_num) v(_num,intrans)VP(_num) v (_num,trans) NP(_1)

Parsing with features (bottom-up)

S NP(_num) VP(_num)

NP(_num) det(_num) n(_num)

the man shot those elephants

NP (sing)

the = det(_num)

det (_num)

the

man = n(sing)

shot = v(sing,trans)

(sing)

S

VP(_num) v (_num,trans) NP(_1)

VP (sing,trans)

those = det(pl)

elephants = n(pl)

n(sing)

man

v(sing,trans)

shotdet (pl)

those

n(pl)

elephants

NP (pl)

10/21

Feature structures

• Instead of attaching features to the symbols, we can parse with symbols made up entirely of attribute-value pairs: “feature structures”

• Can be used in the same way as seen previously• Values can be atomic …• … or embedded feature structures …

CAT NPNUMBER SGPERSON 3

ATTR1 VAL1ATTR2 VAL2ATTR3 VAL3

CAT NP

AGRNUM SGPERS 3

11/21

Feature structures

• … or they can be coindexed

CAT S

HEADAGR 1

SUBJ [ AGR 1 ]

NUM SGPERS 3

12/21

Parsing with feature structures

• Grammar rules can specify assignments to or equations between feature structures

• Expressed as “feature paths”e.g. HEAD.AGR.NUM = SG

CAT S

HEADAGR 1

SUBJ [ AGR 1 ]

NUM SGPERS 3

13/21

Feature unification

• Feature structures can be unified if– They have like-named attributes that have the

same value:

[NUM SG] [NUM SG] = [NUM SG]– Like-named attributes that are “open” get the

value assigned:

CAT NPNUMBER ??PERSON 3

NUMBER SGPERSON 3 =

CAT NPNUMBER SGPERSON 3

14/21

Feature unification

– Complementary features are brought together

– Unification is recursive

– Coindexed structures are identical (not just copies): assignment to one effects all

CAT NPNUMBER SG

[PERSON 3] =CAT NPNUMBER SGPERSON 3

CAT NPAGR [NUM SG]

CAT NP

AGRNUM SGPERS 3

=CAT NPAGR [PERS 3]

15/21

ExampleCAT NPAGR _1 _2SEM _3

CAT DETAGR _1

CAT NAGR _2 SEM _3

CAT DET

AGRVAL INDEFNUM SG

a

CAT DETAGR [VAL DEF]

the

CAT NLEX “man”AGR [NUM SG]SEM HUM

man

16/21

the manthe

CAT NAGR _2 SEM _3

CAT DETAGR [VAL DEF]

the

CAT NPAGR _1 _2SEM [_3]

CAT DETAGR _1 [VAL DEF]VAL DEF

CAT NLEX “man”AGR [NUM SG]SEM HUM

man

LEX “man”AGR [NUM SG]SEM HUM

the man

NUM SGHUM

17/21

a mana

CAT NAGR _2 SEM _3

CAT NPAGR _1

_2

SEM [_3]

CAT DET

AGR _1

CAT NLEX “man”AGR [NUM SG]SEM HUM

man

LEX “man”AGR [NUM SG]SEM HUM

a man

[NUM SG]

HUM

CAT DET

AGRVAL INDEFNUM SG

a

VAL INDEFNUM SG

VAL INDEFNUM SG

VAL INDEFAGR NUM SG

18/21

Types and inheritance

• Feature typing allows us to constrain possible values a feature can have– e.g. num = {sing,plur}– Allows grammars to be checked for consistency, and

can make parsing easier

• We can express general “feature co-occurrence conditions” …

• And “feature inheritance rules”• Both these allow us to make the grammar more

compact

19/21

Co-occurrence conditions and Inheritance rules

• General rules (beyond simple unification) which apply automatically, and so do not need to be stated (and repeated) in each rule or lexical entry

• Examples:[cat=np] [num=??, gen=??, case=??]

[cat=v,num=sg] [tns=pres]

[attr1=val1] [attr2=val2]

20/21

Inheritance rules

• Inheritance rules can be over-riddene.g. [cat=n] [gen=??,sem=??]

sex={male,female}

gen={masc,fem,neut}

[cat=n,gen=fem,sem=hum] [sex=female]

uxor [cat=n,gen=fem,sem=hum]

agricola [cat=n,gen=fem,sem=hum,sex=male]

21/21

Unification in Linguistics

• Lexical Functional Grammar– If interested, see PARGRAM project

• GPSG, HPSG

• Construction Grammar

• Categorial Grammar