Models of Generative Grammar

1. Models of Generative Grammar Smriti Singh

2. 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.

3. 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.

4. 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.

5. 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

6. 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.

7. 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”.

8. 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.

9. 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.

10. 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

11. 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.

12. 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.

13. 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

14. 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.

15. 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.

16. 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

17. 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) :

18. 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.

19. 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

20. 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.

21. 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)