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CONTEXT-FREE GRAMMARS

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Syntactic analysis (Parsing)

S

NP VP

AT NNS VBD NP

AT NNthe children ate

the cake

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Beyond regular languages: Context-Free Grammars

S NP VPNP Det NominalNominal NounVP V

Det theDet aNoun flightV left

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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)

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Derivations and parse trees

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A more formal definition

A CFG is a 4-tuple <N,,P, S> consisting of

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What `context free’ means

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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

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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

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An example lexicon

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An example grammar

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A simple parse tree

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Basic types of phrases

Sentences Noun Phrases Verb phrases Prepositional phrases

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Basic types of sentences

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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

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Noun phases: postmodifiers

Nominal Noun Nominal Nominal PP (PP) (PP) Nominal Nominal GerundVP Nominal Nominal RelClause

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Types of postnominal modifiers

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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)

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Recursion and VP attachment

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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

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Agreement

This dog Those dogs *This dogs *Those dogs This dog is smart *This dog are smart *Those dogs is smart

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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 _?

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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

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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