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CONTEXT-FREE GRAMMARS

CONTEXT-FREE GRAMMARS. Syntactic analysis (Parsing). S. NP. VP. NP. AT. NNS. VBD. the. children. ate. AT. NN. the. cake. Beyond regular languages: Context-Free Grammars. S  NP VP NP  Det Nominal Nominal  Noun VP  V. Det  the Det  a Noun  flight V  left. Derivations.

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CONTEXT-FREE GRAMMARS

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  1. CONTEXT-FREE GRAMMARS

  2. Syntactic analysis (Parsing) S NP VP NP AT NNS VBD the children ate AT NN the cake NLE

  3. Beyond regular languages: Context-Free Grammars S  NP VPNP  Det NominalNominal  NounVP  V Det  theDet  aNoun  flightV  left NLE

  4. Derivations • A DERIVATION of a string is a sequence of rule applications • E.g., the string “a flight” can be derived from the grammar above and symbol NP by the (leftmost first) derivation • NP => Det Nominal => a Nominal => a Noun => a flight • Derivations can be visualized as PARSE TREES • The LANGUAGE defined by a CFG is the set of strings derivable from the start symbol S (for Sentence) NLE

  5. Derivations and parse trees NLE

  6. A more formal definition • A CFG is a 4-tuple <N,,P, S> consisting of NLE

  7. What `context free’ means NLE

  8. Derivations and languages • The language LG GENERATED by a CFG grammar G is the set of strings of TERMINAL symbols that can be derived from the start symbol S using the production rules in G • LG = {w | w is in * and S derives w} • The strings in LG are called GRAMMATICAL • The strings not in LG are called UNGRAMMATICAL NLE

  9. Grammar development • One of the most basic skills in NLE is the ability to write a CFG for some fragment of a language (e.g., the dates) • We’ll briefly cover some of the issues to be addressed when writing small CFG grammars NLE

  10. An example lexicon NLE

  11. An example grammar NLE

  12. A simple parse tree NLE

  13. Basic types of phrases • Sentences • Noun Phrases • Verb phrases • Prepositional phrases NLE

  14. Basic types of sentences NLE

  15. Noun phases: premodifiers • NP  (Det) (Card) (Ord) (Quant) (AP) Nominal • Det: Determiners • a flight • Optional: I’m looking for flights to Denver • Card: Cardinal numbers (one stop) • Ord: Ordinal numbers (the first flight) • Quantifiers: most flights to Denver leave in the morning • AP (Adjectives): three very expensive seats NLE

  16. Noun phases: postmodifiers • Nominal  Noun • Nominal  Nominal PP (PP) (PP) • Nominal  Nominal GerundVP • Nominal  Nominal RelClause NLE

  17. Types of postnominal modifiers NLE

  18. Recursion • Nominal  Nominal PP (PP) (PP) • Is an example of RECURSIVE rule • Other examples: • NP  NP PP • VP  VP PP • Recursion a powerful device, but could have bad consequences (see lectures on parsing) NLE

  19. Recursion and VP attachment NLE

  20. Coordination • NP  NP and NP • John and Mary left • VP  VP and VP • John talks softly and carries a big stick • S  S and / but / S • Kim is a lawyer but Sandy is reading medicine. • In fact, probably English has a • XP  XP and XP rule NLE

  21. Agreement • This dog • Those dogs • *This dogs • *Those dogs • This dog is smart • *This dog are smart • *Those dogs is smart NLE

  22. CFGs vs Regular languages • For many applications, finite state languages (the languages defined by FA) are appropriate • Limitation of FAs: cannot count • I.e., cannot check A n B n • Example of construction showing that English is CF: long-distance dependencies • Which film did Kim say the director who we just met _ recommended _? NLE

  23. The Chomsky Hierarchy • Finite-state languages (type 3) • A  bC | Cb (a single NT on the right) • Context-free languages (type 2) • A  BB • Context-sensitive languages (type 1) • CAC  BB • Recursively enumerable languages • Every language that can be specified by a finite algorithm NLE

  24. Readings • Jurafsky and Martin, chapter 9 • The chapters on context-free languages in • The Free Dictionary: http://encyclopedia.thefreedictionary.com/Context-free%20language • Wikipedia: http://en.wikipedia.org/wiki/Context-free_grammar NLE

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