1 context-free grammars. nle 2 syntactic analysis (parsing) s npvp atnnsvbd np at nnthechildrenate...
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CONTEXT-FREE GRAMMARS
NLE2
Syntactic analysis (Parsing)
S
NP VP
AT NNS VBD NP
AT NNthe children ate
the cake
NLE4
Beyond regular languages: Context-Free Grammars
S NP VPNP Det NominalNominal NounVP V
Det theDet aNoun flightV left
NLE5
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)
NLE6
Derivations and parse trees
NLE7
A more formal definition
A CFG is a 4-tuple <N,,P, S> consisting of
NLE8
What `context free’ means
NLE9
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
NLE10
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
NLE11
An example lexicon
NLE12
An example grammar
NLE13
A simple parse tree
NLE14
Basic types of phrases
Sentences Noun Phrases Verb phrases Prepositional phrases
NLE15
Basic types of sentences
NLE16
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
NLE17
Noun phases: postmodifiers
Nominal Noun Nominal Nominal PP (PP) (PP) Nominal Nominal GerundVP Nominal Nominal RelClause
NLE18
Types of postnominal modifiers
NLE19
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)
NLE20
Recursion and VP attachment
NLE21
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
NLE22
Agreement
This dog Those dogs *This dogs *Those dogs This dog is smart *This dog are smart *Those dogs is smart
NLE24
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 _?
NLE25
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
NLE26
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