Models of generative grammar
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Models of Generative Grammar. 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 -

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Models of Generative Grammar

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Models of Generative Grammar


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.


Models of Generative Grammar

  • Several models of Generative Grammar have been formally investigated following Chomsky’s 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.


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.


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

mencome


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.


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”.


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.


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.


An example of CFG

  • Here's a simple context free grammar for a small fragment of English:

    S -> NP VP

    NP -> Det N

    VP -> V NP

    VP -> V

    Det -> a

    Det -> the

    N -> woman

    N -> man

    V -> shoots


Ingredients and properties of this grammar

  • What are the ingredients of this grammar?

    It contains three types of symbol:

  • ‘->’ = 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.


Rule explanation

  • This grammar contains nine rules.

  • Each rule consists of a single non-terminal symbol, followed by ->, 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.


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


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.


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.


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


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) :


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.


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


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 rulesthat grab phrases or pieces of phrases and move them around in specified ways.


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)


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