Three Models for the Description of Language

3 Phrase structure

1. What is immediate constituent analysis?
   Grouping the words of a sentence into phrases, these into smaller constituent phrases, and so on down to the ultimate constituents (generally morphemes), with phrases classified as NP, VP, etc.
   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
2. Why is constituent analysis simpler than the word-by-word model?
   A complex class of expressions like NP is stated once in the grammar and then used as a building block at various points in sentences.
   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
3. Define a phrase-structure \([\Sigma, F]\) grammar.
   A finite vocabulary \(V_P\), a finite set \(\Sigma\) of initial strings and a finite set \(F\) of rules \(X \to Y\) (“rewrite X as Y”), where Y is formed from X by replacing a single symbol with a string. A derivation is like a proof, with \(\Sigma\) as axioms and \(F\) as rules of inference.
   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
4. Give Chomsky’s small phrase-structure grammar and the tree it assigns to “the man took the book”.
   Σ: # Sentence #. F: Sentence → NP VP; VP → Verb NP; NP → the man, the book; Verb → took.

   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
5. When are two derivations equivalent, and what is a phrase in a derivation?
   Equivalent derivations differ only in the order in which rules are applied and reduce to the same diagram. A substring is an X if it traces back to a single node labelled X: “the man” is an NP, but “man took” is not a phrase at all.
   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
6. What is constructional homonymity? Illustrate with “they are flying planes”.
   A sentence receiving nonequivalent derivations from the simplest grammar. Rules for “they are flying – a plane” and “(flying) planes – are – noisy” give two structures: they – are – [flying planes] (those specks are flying planes) and they – [are flying] – planes (those pilots are flying planes). The formal ambiguity explains the semantic one.

   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
7. How can ambiguity be used to test a grammar’s adequacy?
   Check whether cases of constructional homonymity are actually cases of semantic ambiguity: a revealing grammar gives ambiguous sentences alternative analyses.
   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
8. What refinements to phrase-structure rules does Chomsky mention?
   Context-sensitive rules (rewrite X as Y only in the context Z–W), and ordering the rules in a sequence with obligatory and optional rules; these simplify the grammar without changing its generative power.
   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
9. How do finite-state, derivable and terminal languages relate (Theorem 27)?
   Every finite-state language is a terminal language (generated by a phrase-structure grammar), but not conversely; every derivable language is terminal, but not conversely; some derivable languages aren’t finite-state and some finite-state languages aren’t derivable.
   • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
10. What is the main import of the result that every finite-state language is a terminal language?
    Phrase-structure description is essentially more powerful, not just simpler, than finite-state grammars producing sentences left to right. \(a^n b^n\) is a terminal language (Z → a b, Z → a Z b), so the mirror-image argument against finite-state models doesn’t apply to phrase structure.
    • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
11. Why is phrase structure “more abstract” than the finite-state model?
    Its description uses symbols that aren’t in the language’s vocabulary (\(V_P\) properly includes \(V_T\)): Sentence, NP, VP are not words of English.
    • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
12. In what sense is a phrase-structure grammar still a finite-state process?
    Its state is determined by which initial strings occur in the last string produced, and it moves on by applying a rule to that string: at each point the process depends on its present state and a bounded amount of the last output.
    • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3
13. Does Chomsky reject phrase structure because English is outside its range?
    No: he didn’t know whether English is a terminal language (\(L_3\), copies \(XX\), is not), so he couldn’t disqualify phrase structure on that ground. He rejects it on the complexity of description.
    • Chomsky, 1956, Three Models for the Description of Language (IRE Transactions on Information Theory), §3