Context-Free Parsing

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Context-Free Parsing

• Part 2
• Features and Unification

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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 well see that feature bundles can
  completely replace constituents

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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(numX) VP (numX) NP (numX) ? det(numX)
n (numX) VP(numX) ? v(numX) NP(num?)
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Declarative nature of features

• The 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 (numX) ? det(numX) n (numX)
this det (numsg) these det (numpl) the
det (num?) man n (numsg) men n (numpl)
NP (numsg)
det(numsg) n(numsg)
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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 (numX) ? det(numX) n (numX)
this det (numsg) these det (numpl) the
det (num?) man n (numsg) men n (numpl)
NP (numsg)
det(num?) n(numsg)
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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 position
• e.g. NP(_num,_sem) ? det(_num) n (_num,_sem)
• an det(sing)
• the det(_num)
• man n(sing,hum)

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Parsing with features
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)

• Using features to impose subcategorization
  constraints

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)
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Parsing with features (top-down)
S ? NP(_num) VP(_num) NP(_num) ? det(_num)
n(_num) VP(_num) ? v(_num,intrans) VP(_num) ? v
(_num,trans) NP(_1)
the man shot those elephants
S ? NP(_num) VP(_num)
NP(_num) ? det(_num) n(_num)
the det(_num)
man n(sing)
(sing)
(sing)
_numsing
VP(sing) ? v(sing,intrans)
shot v(sing,trans)
(sing)
(pl)
(sing)
VP(sing) ? v(sing,trans) NP(_1)
shot v(sing,trans)
NP(_1) ? det(_1) n(_1)
(pl)
(pl)
those det(pl)
elephants n(pl)
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ADAPT formalism
s(_fin,_tns) --gt np(_agr,subj),
vp(_agr,_tns,_val). np(_agr,_case) --gt det(_agr),
n(_agr). np(_agr,_case) --gt pro(_agr,_case). np(no
t3sg,_case) --gt n(not3sg). bare
plurals np(3sg,_case) --gt n(mass). mass nouns
can be bare too n(_agr) --gt adj(), n(_agr).
or with noun compounds n(_agr) --gt n(_agr1),
n(_agr). vp(_agr,_tns,_val) --gt
vp(_agr,_tns,_val), pp(). vp(_agr,_tns,_val) --gt
vp(_agr,_tns,_val), adv(). vp(_agr,_tns,intr) --gt
vg(_agr,_tns,intr). vp(_agr,_tns,tr) --gt
vg(_agr,_tns,tr), np(_agr0,obj). _cat() --gt
_cat(), conj(), _cat(). etc

• Note distinction between _variable and value
• Rules always have the same number of arguments
• (or it counts as a different category)
• Even if the value is of no interest
• You can even have variable functor names
• (for those who know Prolog) it looks like
  Prolog, but it aint!

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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

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Feature structures

• or they can be coindexed

CAT S HEAD
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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 HEAD
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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

?

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Feature unification

• Complementary features are brought together
• Unification is recursive
• Coindexed structures are identical (not just
  copies) assignment to one effects all

?

PERSON 3
CAT NP AGR NUM SG
CAT NP AGR PERS 3
?

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Example
CAT N AGR _2 SEM _3
CAT NP AGR _1 ? _2 SEM
_3
CAT DET AGR _1
?
CAT DET AGR
?
a
?
CAT DET AGR VAL DEF
the
CAT N LEX man AGR NUM SG SEM
HUM
?
man
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the man
the
the man
CAT N AGR _2 SEM _3
CAT NP AGR _1
? _2 SEM _3
CAT DET AGR _1
?
LEX man AGR NUM SG SEM HUM
VAL DEF
VAL DEF
NUM SG
HUM
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a man
a
a man
CAT NP AGR _1
? _2 SEM
_3
CAT N AGR _2 SEM _3
CAT DET AGR _1
?
LEX man AGR NUM SG SEM HUM
NUM SG
HUM
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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

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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
• catnp ? num??, gen??, case??
• catv,numsg ? tnspres
• attr1val1 ? ? attr2val2

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Inheritance rules

• Inheritance rules can be over-ridden
• e.g. catn ? gen??,sem??
• sexmale,female
• genmasc,fem,neut
• catn,genfem,semhum ? sexfemale
• uxor catn,genfem,semhum
• agricola catn,genfem,semhum,sexmale

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Unification in Linguistics

• Lexical Functional Grammar
• If interested, see PARGRAM project
• GPSG, HPSG
• Construction Grammar
• Categorial Grammar