Chapter 16: Features and Unification

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Chapter 16 Features and Unification

• 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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Agenda

• we introduce the idea that grammatical categories
  like VPto, Sthat, Non3sgAux, or 3sgNP, as well as
  the grammatical rules like S?NP VP that make use
  of them, should be thought of as objects that can
  have complex sets of properties associated with
  them
• The information in these properties is
  represented by constraints, and so these kinds of
  models are often called constraint based
  formalisms
• Use these constraints for
• Agreement (this flights)
• Subcategorization ()
• Adding properties (features) to words
• Adding some operation to rules in order to test
  equalities

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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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examples
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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
• 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 (Reentrant)
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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

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Unification with Reentrancies

• When unification takes place, shared values are
  copied over

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example
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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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Subsumption

• F ? G if and only if
• 1. For every feature x in F, F(x) ? G(x) (where
  F(x) means the value of the feature x of feature
  structure F).
• 2. For all paths p and q in F such that F(p)
  F(q), it is also the case that G(p) G(q).

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Subsumption
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Subsumption (partial order)
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Semilattice, unification

• ?F ? F , so we can model the sumsumption as a
  lattice , which at the top of it
• Unification F?G most general H such that F ? H
  and G ? H

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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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FEATURES STRUCTURES IN THE GRAMMAR
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agreement

• subject-verb agreement and determiner nominal
  agreement.

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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
• 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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agreement
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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
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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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Subcategorization frame
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Long Distance Dependencies

• What cities does Continental service?
• What flights do you have from Boston to
  Baltimore?
• What time does that flight leave Atlanta?
• wh-non-subject-question
• S ? Wh-NP Aux NP VP
• Should WH-NP agreed with NP
• Gap-list implemented by feature GAP are
  passed through different trees
• Fillers (what cities) are put on the top of gap
  list and should be unified to the
  subcategorization frame of the verb

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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

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Overview

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

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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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• Base case
• One or both of the arguments has a null value.
• The arguments are identical.
• The arguments are non-complex and non-identical.

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An Example
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• original arguments are neither identical, nor
  null, nor atomic,
• These arguments are also non-identical, non-null,
  and non-atomic so the loop is entered again
  leading to a recursive check of the values of the
  AGREEMENT features

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f1 and f2 after the recursion adds the value of
the new PERSON feature
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The final structures of f1 and f2 at the end
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Modifying a Early 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 Parser with Unification
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Predictor, Scanner, Completer
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Unify States
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Example (That flight )
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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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The Need for Copying

• show me morning flights

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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

• 16.2, 16.3, 16.6, 16.7,