Chapter 11: Parsing with Unification Grammars

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Chapter 11 Parsing with Unification Grammars

• Heshaam Faili
• hfaili_at_ece.ut.ac.ir
• University of Tehran

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Overview

• Feature Structures and Unification
• Unification-Based Grammars
• Chart Parsing with Unification-Based Grammars
• Type Hierarchies

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Feature structures

• We had a problem adding agreement to CFGs. What
  we needed were features, e.g., a way to say
• number sg
• person 3
• A structure like this allows us to state
  properties, e.g., about a noun phrase
• cat NP
• number sg
• person 3
• Each feature (e.g., number) is paired with a
  value (e.g., sg)
• A bundle of feature-value pairs can be put into
  an attribute-value matrix (AVM)

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Feature paths

• Values can be atomic (e.g. sg or NP or 3),
  or can be complex, and thus we can define feature
  paths
• cat NP
• agreement number sg
• person 3
• The value of the path agreement number is sg
• A grammar with only atomic feature values can be
  converted to a CFG.
• e.g. AVM on previous page ? NP3,sg
• However, when the values are complex, it is more
  expressive than a CFG ? can represent more
  linguistic phenomena

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An Example for FS
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Reentrancy (structure-sharing)

• Feature structures embedded in feature structures
  can share the same values
• That is, two features have the exact same
  valuethey share precisely the same object as
  their value
• well indicate this with a tag like 1
• cat S
• head agr 1num sg
• per 3
• subj agr 1
• In this example, the agreement features of both
  the matrix sentence and the embedded subject are
  identical
• This is referred to as reentrancy

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FS with shared value
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Feature structures as graphs

• Technically, feature structures are directed
  acyclic graphs (DAGs)
• So, the feature structure represented by the
  attribute-value matrix (AVM)
• cat NP
• agreement number sg
• person 3
• is really the graph

CAT
np
?
?
sg
NUM
?
AGR
PER
?
?
3
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Unification

• Unification (U) a basic operation to merge two
  feature structures into a resultant feature
  structure (FS)
• The two feature structures must be compatible,
  i.e., have no values that conflict
• Identical FSs
• number sg U number sg number sg
• Conflicting FSs
• number sg U number pl Fail
• Merging with an unspecified FS
• number sg U number number sg

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Unification (cont.)

• Merging FSs with different features specified
• number sg U person 3 number sg
  
• person 3
• More examples
• cat NP U agreement number sg
• cat NP
• agreement number sg
• agr num sg
• subj agr num sg U subj
  agr num sg
• agr num sg
• subj agr num sg

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Unification with Reentrancies

• Remember that structure-sharing means they are
  the same object
• agr 1num sg U subj agr per 3
• per 3
  num sg
• subj agr 1
• agr 1 num sg
• per 3
• subj agr 1
• When unification takes place, shared values are
  copied over
• agr 1 U sub agr per 3
• subj agr 1 num
  sg
• agr 1
• subj agr 1per 3
• num sg

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Unification with Reentrancies (cont.)

• And remember that having similar values is not
  the same as structure-sharing
• agr num sg U sub agr
  per 3
• subj agr num sg
  num sg
• agr num sg
• subj agr per 3
• num sg
• With structure-sharing, you have to make sure the
  values are compatible everywhere that
  structure-sharing is specified
• agr 1num sg U agr num sg
• per 3 per 3 Fail
• subj agr 1 subj agr num pl
• per 3

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Subsumption

• We can see that a more general feature structure
  (less values specified) subsumes a more specific
  feature structure
• (1) num sg
• (2) per 3
• (3) num sg
• per 3
• So, we have the following subsumption relations,
  where
• (1) subsumes (3)
• (2) subsumes (3)
• (1) does not subsume (2), and (2) does not
  subsume (1)

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Implementing Unification

• How do we implement a check on unification?
• i.e., given feature structures F1 and F2, return
  F, the unification of F1 and F2
• Unification is a recursive operation
• If a feature has an atomic value, see if the
  other FS has that feature with the same value
• F a unifies with , F , and F a
• If a feature has a complex value, follow the
  paths to see if theyre compatible and have the
  same values at bottom
• Does F G1 unify with F G2? We have to
  inspect G1 and G2 to find out.
• To avoid cycles, we have to do an occur check to
  see if weve seen a FS before or not

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Overview

• Feature Structures and Unification
• Unification-Based Grammars
• Chart Parsing with Unification-Based Grammars
• Type Hierarchies

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Grammars with Feature Structures

• CFG skeleton augmented with feature structure
  path equations, i.e., each category has a feature
  structure
• CFG skeleton
• S ? NP VP
• Path equations
• ltNP agreementgt ltVP agreementgt
• 1. There can be zero or more path equations for
  each rule skeleton ? no longer atomic
• 2. When a path equation references constituents,
  they can only be constituents from the CFG rule
• e.g., ltD agreementgt ltNom agreementgt is an
  illegal equation for the above rule! (But it
  would be fine for NP ? Det Nom)

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Agreement in Feature-Based Grammars

• S ? NP VP
• ltS headgt ltVP headgt
• ltNP head agrgt ltVP head agrgt
• VP ? V NP
• ltVP headgt ltV headgt
• NP ? Det Nom(inal)
• ltNP headgt ltNom headgt
• ltDet head agrgt ltNom head agrgt
• Nom ? Noun
• ltNom headgt ltNoun headgt
• Noun ? flights
• ltNoun head agr numgt pl

• Compare with the CFG case
• S ? 3sgNP 3sgVP
• S ? PluralNP PluralVP
• 3sgVP? 3sgVerb
• 3sgVP ? 3sgVerb NP
• 3sgVP ? 3sgVerb NP PP
• 3sgVP ? 3sgVerb PP
• etc.

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Percolating Agreement Features

• S ? NP VP
• ltNP head agrgt ltVP head agrgt
• VP ? V NP
• ltVP headgt ltV headgt
• NP ? Det Nom
• ltNP headgt ltNom headgt
• ltDet head agrgt ltNom head agrgt
• Nom ? Noun
• ltNom headgt ltNoun headgt

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Head features in the grammar

• An important concept shown in the previous rules
  is that heads of grammar rules share properties
  with their mothers
• VP ? V NP
• ltVP headgt ltV headgt
• Knowing the head will tell you about the whole
  phrase
• This is important for many parsing techniques

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Sub-categorization

• We could specify subcategorization like so
• VP ? V
• ltVP head subcatgt intrans
• VP ? V NP
• ltVP head subcatgt trans
• VP ? V NP NP
• ltVP head subcatgt ditrans
• But values like intrans do not correspond to
  anything that the rules actually look like
• To make SUBCAT better match the rules, we can
  make it a list of a verbs arguments, e.g. ltNP,PPgt

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Handling Subcategorization
head 1subcat lt 2, 3gt

• VP ? V NP PP
• ltVP headgt ltVerb headgt
• ltVP head subcatgt ltNP,PPgt
• V ? leaves
• ltV head agr numgt sg
• ltV head subcatgt ltNP,PPgt
• There is also a longer, more formal way to
  specify lists
• ltNP,PPgt is equivalent to
• FIRST NP
• REST FIRST PP
• REST ltgt

VP
PP
V
NP
cat 2
cat 3
leaves
head 1agr num sg subcat lt
cat np, cat pp gt
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Subcategorization frames

• Subcategorization, or valency, or dependency is a
  very important notion in capturing syntactic
  regularity And there is a wide variety of
  arguments that a verb (or noun or adjective) can
  take.
• Some subcategorization frames for ask
• He asked Q What was it like?
• He asked Swh what it was like
• He asked NP her Swh what it was like
• He asked VPto to see you
• He asked NP her VPto to tell you
• He asked NP a question
• He asked NP her NP a question

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Long-Distance Dependencies

• What is the earliest flight that you have _?

• TOP (fill gap)
• S ? WH-word Be-copula NP
• ltNP gapgt ltWH-word headgt
• MIDDLE (pass gap)
• NP ? D Nom
• ltNP gapgt ltNom gapgt
• Nom ? Nom RelClause
• ltNom gapgt ltRelClause gapgt
• RelClause ? RelPro NP VP
• ltRelClause gapgt ltVP gapgt
• BOTTOM (identify gap)
• VP ? V
• ltVP gapgt ltV subcat secondgt

S
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Overview

• Feature Structures and Unification
• Unification-Based Grammars
• Chart Parsing with Unification-Based Grammars
• Type Hierarchies

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Modifying a Chart Parser to handle Unification

• Our grammar still has a context-free backbone, so
  we could just parse a sentence with a CFG and use
  the features to filter out the ungrammatical
  sentences
• But by utilizing unification as we parse, we can
  eliminate parses that wont work in the end
• e.g., well eliminate NPs that dont match in
  agreement features with their VPs as we parse,
  instead of ruling them out later

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Changes to the Chart Representation

• Each state will be extended to include the LHS
  DAG (which can get augmented as it goes along).
• i.e., Add a feature structure (in DAG form) to
  each state
• So, S ? ? NP VP, 0,0
• Becomes S ? ? NP VP, 0,0, DagS
• The predictor, scanner, and completer have to
  pass in the DAG, so all three operations have to
  be altered

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Earley Chart Parser with Unification
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Predictor

• The predictor starts with the DAG from the
  context-free rule
• S ? NP VP
• ltS headgt ltVP headgt
• ltNP head agrgt ltVP head agrgt
• PREDICTOR
• S ? ? NP VP, 0,0, dagS
• where dagS is
• S head 1
• NP head agr 2
• VP head 1agr 2

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Completer

• The completer combines two rules and unifies the
  two feature structures associated with them
• COMPLETER
• When an NP is completed, the DagS will get
  updated
• S ? NP ? VP, 0,1, DagS
• where DagS is now
• S head 1
• NP definite yes
• head lex students
• agr 2num pl
• VP head 1 agr 2

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Predictor, Scanner, Completer
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Unify States
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Change to ENQUEUE

• The enqueue procedure should also be changed to
  use a subsumption test
• Do not add a state to the chart if an equivalent
  or more general state is already there.
• So, if Enqueue wants to add a singular
  determiner state at x, y, and the chart already
  has a determiner state at x, y unspecified for
  number, then Enqueue will not add it.

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Why a Subsumption Test?

• If we don't impose a subsumption restriction,
  enqueue will add two states at x, y, one
  expecting to see a singular determiner, the other
  just a determiner.
• On seeing a singular determiner, the parser will
  advance the dot on both rules, creating two edges
  (since singular will unify with both singular and
  with unspecified).
• As a result, we would get duplicate edges.
• If we impose the restriction, and we see either a
  single or plural determiner, and we advance the
  dot, only one edge (singular or plural) gets
  created at x, y.

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Overview

• Feature Structures and Unification
• Unification-Based Grammars
• Chart Parsing with Unification-Based Grammars
• Type Hierarchies

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Using Type Hierarchies

• Instead of simple feature structures, formalisms
  like Head-Driven Phrase Structure Grammar (HPSG)
  use typed feature structures
• Two problems right now
• What prevents us right now from specifying the
  following?
• ltnumber femininegt
• How can we capture the fact that all values of
  NUMBER are the same sort of thing, i.e., make a
  generalization?
• Solution use types

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Type Systems

• 1. Each feature structure is labeled by a type.
• noun
• CASE case
• 2. Each type has appropriateness conditions
  specifying what features are appropriate for it.
• noun ? CASE case
• verb ? VFORM vform
• 3. Types are organized into a type hierarchy.
• 4. Unification is modified to allow two different
  types to unify.

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Simple Type Hierarchy
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Type Hierarchy

• So, if
• CASE is appropriate for noun, and
• the value of CASE is case, and
• we have the following type hierarchy
• case
• nom acc dat
• Then, the following are possible feature
  structures
• noun noun noun
• CASE nom CASE acc CASE dat

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Unification of types

• Now, when we unify feature structures, we have to
  unify types, too
• CASE case U CASE nom CASE nom
• CASE nom U CASE acc fail
• Lets also assume that acc and dat have a common
  subtype, obj
• acc dat
• obj
• Then, we have the following unification
• CASE acc U CASE dat CASE obj

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Practices

• 11.2, 11.7, 11.8