Models of Generative Grammar

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Models of Generative Grammar

• Smriti
  Singh

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Generative Grammar

• A Generative Grammar is a set of formal rules
  that can generate an infinite set of sentences
  that constitute the language as a whole.
• Chomsky insisted that a grammar -
• Must systematically describe all of the sentences
  in a language that a native speaker would regard
  as grammatical.
• Must sort out all of the possible "good"
  sentences from all of the possible "bad" ones.
• Must use a finite set of rules.
• Must provide a way to account for our perceived
  ambiguity of certain sentences.

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Models of Generative Grammar

• Several models of Generative Grammar have been
  formally investigated following Chomskys initial
  discussion of
• Finite State Grammars
• Phrase Structure Grammars and
• Transformational Grammars
• Chomsky reviewed the two conceptions of grammar
  (1957)
• The simpler of the two, finite-state grammars,
  are the rule systems that strung words together,
  one by one, and acknowledge no larger phrase
  structure.
• More complex than finite-state grammars are
  grammars called phrase structure grammars that
  build up phrases out of words and put the phrases
  together into sentences.

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Finite State Machine

• Suppose we have a machine
• That has a finite number of different internal
  states -
• One of these states is an initial state and
• Another is a final state.
• That switches from one state to another by
  producing a symbol.
• That begins in the initial state, runs through a
  sequence of states and ends in the final state.

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Finite State Machine (contd.)

• Representing Grammar/machine that produces just
• the two sentences the man comes and the man
• come.
• State Diagram
• man
  comes
• The
• men
  come

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Finite State Grammar

• Each node in the diagram corresponds to a state.
• The sequence of words that has been produced is a
  sentence.
• Such machine defines a certain language the set
  of sentences that can be produced in this way.
• Language produced by such a machine is called a
  finite state language.
• Machine that produces such a language is called a
  finite state grammar.
• FSG is the simplest type of grammar which, with a
  finite amount of apparatus, can generate an
  infinite number of sentences.

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Properties of Finite State Grammars

• Such grammars allow transition from one state to
  another.
• Each state represents the grammatical
  restrictions that limit the choice of the next
  word.
• We can have any number of closed loops of any
  length.
• Machines that produce languages in this manner
  are also known as finite state Markov processes.

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Problems with FSGs

• As all languages are not finite state languages,
  it is impossible to produce all and only the
  grammatical sentences of a language.
• There are processes that FSGs are not equipped to
  handle.

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Context Free Grammar

• In both linguistics and computer science, we are
  not merely interested in whether a string is
  grammatical or not, we want to know why it is
  grammatical.
• CFG is a finite collection of rules which tells
  us that certain sentences/strings are grammatical
  and what their grammatical structure is.
• A context free grammar is one in which all the
  rules apply regardless of the context i.e. they
  would be of the type Rewrite X as Y, no further
  conditions being specified.

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An example of CFG

• Here's a simple context free grammar for a small
  fragment of English
• S -gt NP VP
• NP -gt Det N
• VP -gt V NP
• VP -gt V
• Det -gt a
• Det -gt the
• N -gt woman
• N -gt man
• V -gt shoots

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Ingredients and properties of this grammar

• What are the ingredients of this grammar?
• It contains three types of symbol
• -gt An instruction to rewrite whatever symbol
  appears to the left of the arrow as the symbol or
  string of symbols that appears to the right of
  the arrow.
• Symbols written like S, NP, VP, Det, N, V. These
  symbols are called non-terminal symbols. Each of
  these symbols is shorthand for a grammatical
  category.
• Symbols in italics a, the, woman, man, and
  shoots. A computer scientist would probably call
  these terminal symbols and linguists would
  probably call them lexical items.
• Why Context Free?
• As only single non-terminals occur on the left
  side of the rules.

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Rule explanation

• This grammar contains nine rules.
• Each rule consists of a single non-terminal
  symbol, followed by -gt, followed by a finite
  sequence made up of terminal and/or non-terminal
  symbols.
• We interpret each rule X Y as the instruction
  rewrite X as Y.
• For example, rule (2) rewrites the symbol VP as
  the string of symbols Verb NP, and defines Verb
  NP to be a construction of the type VP.
• The symbol S (for "sentence") is designated as
  the initial symbol.
• It is necessary to begin with a rule that has the
  initial symbol on the left.
• Thereafter any rule may be applied in any order
  until no further rule is applicable.

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Context Free Grammar (contd.)

• Consider the string of words a woman shoots a
  man.
• Is this grammatical according to our little
  grammar?
• And if it is, what structure does it have?
• The following tree answers both the questions
• Such a tree is called a parse tree, and it gives
  us two sorts of
• information
• 1. Information about strings 2. Information
  about structure

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Problems with CFGs

• A context free language is a language that can be
  generated by a context free grammar.
• Some languages are context free, and some are not
  e.g. it seems plausible that English is a context
  free language.
• Some dialects of Swiss-German are not context
  free.
• It can be proved mathematically that no context
  free grammar can generate all (and only) the
  sentences that native speakers find acceptable
  and..
• For such dialects, one needs to employ additional
  grammatical mechanisms, not merely context free
  rules.

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Phrase Structure Grammar

• It builds up phrases out of words and put the
  phrases together into sentences.
• The kind of structural description assigned by a
  phrase-structure grammar is, in fact, an
  immediate constituent analysis of the sentence.
• It assigns to each sentence that it generates a
  structural description.
• It makes use of phrase structure rules.

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Phrase Structure Grammar (contd.)

• It enables us to express patterns of
  grammaticality.
• It provides a structural description to
  characterize the notion of grammaticality.
• It provides a way to capture our intuitions about
  the constituent structure of sentences
• It also provides a way to explain, or account
  for, our perceived ambiguity of certain sentences
  e.g. mistrust wounds
• S S
• NP VP VP
  NP
• N V V
  N
• Mistrust wounds Mistrust
  wounds

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An example of a Phrase Structure Grammar

• It generates and thereby defines as grammatical
  such sentences as "The man will hit the ball"
• An example of a PSG (associated with
  constituent analysis)

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Derivation of a given sentence

• Interpret each rule X Y as rewrite X as Y.
• Derive the sentence the man hit the ball using
  the given grammar
• The numbers at the right of each line refer to
  the rule of the grammar used in constructing that
  line from the preceding line.

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Representation using a Tree Diagram

• The derivation of the last sentence using a Tree
  diagram
• S
• NP
  VP
• Det N Verb
  NP
• 
  
• 
  Det N
• The man hit the
  ball
• Such a tree does not tell in what order the rules
  have been applied.
• Given a derivation of the sentence, its tree
  diagram can be constructed but not vice versa.
• A tree diagram retains just what is essential in
  the derivation for determining the constituent
  analysis.
• The sequence of words can be traced back to a
  single point of origin S

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Inadequacies of PSG

• Although Chomsky found phrase-structure grammar
  to be necessary, he
• argued that this was not sufficient.
• It under-generates i.e. fails to generate all the
  grammatical sentences of the language e.g.
• He burst into a loud cry and left the room.
• The man was bitten by the dog.
• Did the dog bite the man?
• Was the man bitten by the dog?
• 2. It over-generates. It blindly allows many
  sentences as grammatical which are in fact
  ungrammatical e.g.
• The boy died Bill.
• The men would put the book.
• Not all cases of ambiguity are accounted for by
  such Grammar.
• To account for such phenomena, the grammar must
  also include special transformational rules that
  grab phrases or pieces of phrases and move them
  around in specified ways.

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References

• Noam Chomsky. Syntactic Structures. The Hague
  Mouton Co., 1957
• David Crystal. A Dictionary of Linguistics and
  Phonetics (Blackwell, 1984)
• Noam Chomsky. Aspects of the Theory of Syntax
  (Cambridge, MA MIT Press 1965)