7' Parsing in functional unification grammar

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7. Parsing in functional unification grammar

• Han gi-deuc

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Contents

• 7.1 Functional unification grammar
• 7.1.1 Compilation
• 7.1.2 Attributes and values
• 7.1.3 Unification
• 7.1.4 Patterns and constituent sets
• 7.1.5 Grammar
• 7.2 The parser
• 7.2.1 The General Syntactic Processor
• 7.2.2 The parsing grammar
• 7.3 The compiler
• 7.4 Conclusion

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7.1 functional unification grammar

• The claim that this theory makes on the word
  functional in its title is therefore supported
  in three ways.
• 1. It gives primary status to those aspects of
  language that have often been called functional
  logical aspects are not privileged
• 2. It describes linguistic structures in terms of
  the function that a part fills in a whole, rather
  than in terms of parts of speech and ordering
  relations
• 3. Most important for this paper, it requires its
  grammars to function that is, they must support
  the practical enterprises of language generation
  and analysis.

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7.1.1 Compilation

• This paper will concentrate on how this
  translation is actually carried out it will, in
  short, be about machine translation between
  grammatical formalisms.
• This kind of translation to be explored here is
  known in computer science as compilation, and the
  computer program that does it is called a
  compiler.
• The term compilation almost always refers to a
  process that translates a text produced by a
  human into a text that is functionally
  equivalent, but not intended for human
  consumption.

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7.1.2 Attributes and values

• Functional unification grammar knows things by
  their functional descriptions, (FDs). A simple FD
  is a set of descriptors and a descriptor is a
  constituent set, a pattern, or an attribute with
  an associated value.
• The list of descriptors that make up an FD is
  written in square brackets, no significance
  attaching to the order. The attributes in an FD
  must be distinct from one another so that if an
  FD F contains the attribute a, it is always
  possible to use the phrase the a of F to refer
  unambiguously to a value.
• An attribute is a symbol, that is, a string of
  letters. A value is either a symbol or another FD

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7.1.2 Attributes and values

• The sentence He saw her

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7.1.3 Unification

• A string of atoms enclosed in angle brackets
  constitutes a path and there is at least one that
  identifies every value in an FD.
• The path lta1 a2 akgt identifies the value of
  the attribute ak in the FD that is the value of
  lta1 a2 ak-1gt. It can be read as The ak of the
  ak-1 of the a1.
• Paths are always interpreted as beginning in the
  largest FD that encloses them.
• A pair consisting of a path in an FD and the
  value that the path leads to is a feature of the
  object described.
• If the value is a symbol, the pair is a basic
  feature of the FD

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7.1.3 Unification

• The sentence He likes writing books
• Example of Path

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7.1.3 Unification

• The union of a pair of FDs in not, in general, a
  well-formed FD.
• The reason is this The requirement that a given
  attribute appear only once in an FD implies a
  similar constraint on the set of features
  corresponding to an FD.
• A path must uniquely identify a value.

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7.1.3 Unification

• When two or more simple FDs are compatible, they
  can be combined into one simple FD describing
  those things that they both describe, by the
  process of unification.
• Unification is the same as set union except that
  it yields the null set when applied to
  incompatible arguments.
• The sign is used for unification, so that a
  ß denotes the result of unifying a and ß.
• Unification is the fundamental operation
  underlying the analysis and synthesis of
  sentences using functional unification grammar.

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7.1.3 Unification

• Example of Unification

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7.1.4 Patterns and constituent sets

• The value of SUBJ is the FD of a constituent of
  the sentence, whereas the value of ASPECT is not
• The purpose of constituent sets and patterns is
  to identify constituents and to state constraints
  on the order of their occurrence
• The value of the C-set attribute covers all
  constituents.

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7.1.4 Patterns and constituent sets

• Each pattern is a list whose members can be
• 1. A path. The path may have as its valuea. An
  FD. As in the case of the constituent set, the FD
  describes a constituentb. A pattern. The pattern
  is inserted into the current one at this point
• 2. A string of dots. This matches any number of
  constituents
• 3. The symbol . This matches any one constituent
• 4. An FD. This will match any constituent whose
  description is unifiable with it. The unification
  is made with a copy of the FD in the pattern,
  rather than with the FD itself, because the
  intention is to impute its properties to the
  constituent, but not to unify all the
  constituents that match this part of the pattern
• 5. An expression of the form ( fd), where fd is
  an FD. This matches zero or more constituents,
  provided they can all be unified with a copy of
  fd.

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7.1.4 Patterns and constituent sets
Expressions of pattern
The pattern (16) requires exactly one constituent
to have the property TRACENP all others must
have the property TRACENONE
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7.1.5 Grammar

• A functional unification grammar is a single FD
• Example (19) shows a simple grammar,
  corresponding to a context-free grammar
  containing the single rule (20)

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7.2 The Parser

• 7.2.1 The General Syntactic Processor
• The input is an FD that constitutes the
  specification of a sentence to be uttered
• There are two principal data structures, the
  chart and the agenda
• The chart is a directed graph each of whose edges
  maps onto a substring of the sentence being
  analyzed

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7.2.1 The General Syntactic Processor

• Chart
• K1 vertices for a sentence of k words
• Each word in the sentence to be parsed is
  represented by an edge labeled with an FD
  obtained by looking that word up in the lexicon
• If the word is ambiguous, that is, if it has more
  than one FD, it is represented by more than one
  edge.
• All the edges for the i-th word clearly go from
  vertex i 1 to vertex i
• The label on an active edge has two parts, an FD
  describing what is known about the putative
  phrase, and a procedure that will carry the
  recognition of the phrase one step further forward

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7.2.1 The General Syntactic Processor

• Parsing proceeds in a series of steps in each of
  which the procedure on an active edge is applied
  to a pair of FDs, one coming from that same
  active edge, and the other from an inactive edge
  that leaves the vertex where the active edge
  ends.
• If a and i are an active and an inactive edge
  respectively, a being incident to the vertex that
  i is incident from, the step consists in
  evaluating Pa(fa,fi) , where fa and fi are the
  FDs on a and i, and Pa is the procedure

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7.2.1 The General Syntactic Processor

• This process carried out for every pair
  consisting of an active followed by an inactive
  edge that comes to be part of the chart. Each
  successful step leads to the introduction of one
  new edge, but this edge may result in several new
  pairs.
• Each new pair produced therefore becomes a new
  item on the agenda which serves as a queue of
  pairs waiting to be processed

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7.2.2 The parsing grammar

• The parsing grammar, as we have seen, takes the
  form of a set of procedures, each of which
  operates on a pair of FDs
• One of these FDs, the matrix FD, is a partial
  description of a phrase, and the other, the
  constituent FD, is as complete a description as
  the parser will ever have of a candidate for
  inclusion as constituent of that phrase

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7.2.2 The parsing grammar
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7.3 The compiler

• The compiler has two major sections. The first
  part is a straightforward application of the
  generation program to put the grammar,
  effectively, into disjunctive normal form. The
  second is concerned with actually building the
  procedures
• If F is grammar, or indeed any complex FD, it is
  always possible to recast it in the form F1 ? F2
  Fn, where the Fi (1 i n) each contain no
  alternations

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7.3 The compiler

• The process of generation from a particular FD,
  , effectively selects those members of F1 Fn
  that can be unified with , and then repeats this
  procedure recursively for each constituent. F is,
  in general, a conjunct containing some atomic
  terms and some alternations.

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7.3 The compiler

• Ignoring patterns for the moment, the procedure
  is as follows
• 1. Unify the atomic terms of F with . If this
  fails, the procedure as a whole fails. Some
  number of alternations now remain to be
  considered. In other words, that part of F that
  remains to be unified with is an expression F'
  of the form (a1.1 ? a1.2 a1.k1) (a2.1 ? a2.2
  a2.k2) (an.1 ? an.2 an.kn)
• 2. Rewrites as an alternation by multiplying out
  the terms of an arbitrary alternation in F', say
  the first one. This give an expression F" of the
  form (a1.1 (a2.1 ? a2.2 a2.k2) (an.1 ? an.2
  an.kn)) ? (a1.2 (a2.1 ? a2.2 a2.k2) (an.1
  ? an.2 an.kn)) ? (a1.k1 (a2.1 ? a2.2
  a2.k2) (an.1 ? an.2 an.kn))
• 3. Apply the whole procedure (steps 1-3)
  separately to each conjunct in F"

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7.3 The compiler

• It remains to spell out the alternatives that are
  implicit in the patterns
• The basic idea is to generate all permutations of
  the constituent set of the FD and to eliminate
  those that do not match all the patterns
• The result of this phase of the compilation is a
  list of simple FDs, containing no alternations,
  and having either no pattern, or a single
  pattern that specifies the order of constituents
  uniquely
• Those that have no pattern become lexical entries
  and they are of no further interest to the
  compiler

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7.3 The compiler

• The second phase of the compiler centers around a
  procedure which, given a list of simple FDs, and
  an integer n, attempts to find an attribute, or
  path, on the basic of which the nth constituent
  of those FDs can be distinguished
• The result of this process is (1) a path A, (2) a
  set of values for A, each associated with the
  subset of the list of FDs whose nth constituent
  has that value of A, and (3) a residual subset of
  the list consisting of FDs whose nth constituent
  has no value of the attribute A

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7.3 The compiler

• Second process

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7.4 Conclusion

• Two things can be said to mitigate this to some
  extent. First, the parsing and generation
  grammars do indeed describe exactly the same
  languages, so that much of the work involved in
  testing prototype grammars can be done with a
  generator that works directly and efficiently off
  the competence grammar. The second point is this
  the compiler behaves as though any
  attribute-value pair in the grammar that did not
  mention CAT was not there at all.
• The resulting set of parsing procedures clearly
  recognizes at least all the sentences of the
  language intended, though possibly others in
  addition.