ContextFree Grammars for English

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Context-Free Grammars for English
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What are grammars used for in CL?

• Grammar checking
• Natural Language Understanding
• (1) HP fired Carlini.
• (2) Carlini was fired by HP.
• (3) The most recent executive to be fired by HP
  was Carlini.
• (4) Carlini was the most recent executive to be
  fired by HP.
• (1)-(4) all convey the same basic fact, but you
  need to know the grammatical relationship among
  these sentences to capture that.
• This sort of info is used in Machine Translation,
  Question-Answering, Information Extraction, etc.

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Grammars, Recognition and Parsing
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Sentence Recognition vs. Sentence Parsing

• Recognizer
• ?- recognize(the,girl,waved).
• yes
• ?- recognize(waved,girl,the).
• no
• Parser
• ?- parse(the,girl,waved,Parse).
• Parse det,n,vi
• yes

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A Sentence Grammar vs. A Sentence Parser

• Grammar - a systematic description of the
  structures that underlie the sentences of a
  language
• Parser - a program for determining the structures
  for particular sentences
• capitalizes on the fact that an infinite number
  of sentences can be captured with a finite number
  of structures

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Grammar vs. Recognizer Parser

• A Grammar is a declarative description
• It states the conditions for a string to be
  valid.
• A Recognizer is a procedural process.
• It determines whether a particular sentence is
  valid.
• A Parser is a procedural process.
• It determines what the structure of a
  particular sentence is.

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The Chomsky Hierarchy

• Chomsky (1959) identified four classes of
  grammars in terms of their constraints
• Unrestricted phrase structure grammars (type 0)
• Context-sensitive grammars (type 1)
• Context-free grammars (type 2)
• Regular grammars (type 3)
• Higher numbered types are more constrained and so
  can generate a smaller set of languages.

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Why look at grammar types?

• More constrained grammars will be easier to write
  and compute with.
• Question here What is the most constrained
  grammar that can be used to describe a natural
  language?

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Automata theory formal languages and formal
grammars
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We looked at Regular Grammars in Chapter 2

• Left regular grammars have rules of the form
• A ? a (A is non-terminal a is terminal)
• A ? Ba
• A ? e (e is the empty string)
• Right regular grammars have rules of the form
• A ? a
• A ? aB
• A ? e

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Finite State Grammars

• Regular grammars are also called finite state
  grammars, which we saw used for morphological
  analysis
• In a regular grammar, or FSA, the only
  information we need to know to generate or
  recognize a sentence is the state we are in.
• We do not need to know anything about what we
  have already traversed in order to finish the
  sentence.

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A Finite State Grammar
adj

adj
n
det
vi
3
n
Pn/pro
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One Configuration ofA Finite State Automaton

• Many buildings collapsed

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• Pointer begins in an initial state.
• It moves through a finite set of states.
• As it moves it usually
• scans a new word
• transitions from one state to the next
• It ends in a pre-designated final state.

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A Finite State Grammar-based Recognizer

• If the recognition procedure can find a
• det
• or adj
• or Pn
• or pro
• it can move from state 1 to
• state 2 (if det)
• state 3 (if adj)
• state 4 (if Pn or pro)

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Representing the FS Transitions -a Prolog
example-

• Grammar
• arc(1,det,2).
• arc(2,adj,3).
• arc(1,adj,3).
• arc(1,pro,4).
• arc(1,Pn,4).
• initial(1).
• final(6).

• Lexicon
• word(the,det).
• word(girl,n).
• word(slept,vi).
• word(she,pro).
• word(saw,n).
• word(saw,vi).
• fstn wksht

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Problem with FSA/Regular Grammars

• Cannot handle long-distance dependencies
• If S1 then S2
• Either S1 or S2
• The man who said that S1 is arriving tomorrow.
• Does not recognize phrasal constituency
• (Det N is an NP)
• Chomsky, 1957.

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Context-free Grammars
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CFG Rules allow center embedding

• S ? a S b
• S ? e
• This grammar generates the language
• an bn n 0
• which is not regular.

• S
• a S b
• a S b
• e

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Context-Free Grammars

• Used extensively to describe both formal
  (programming) and natural languages
• Also referred to as Phrase Structure Grammars
• Presented with a BNF (Backus Naur Form)
  notation
• ltSgt ltagt ltSgt ltbgt
• ltSgt e
• also referred to as Backus Normal Form

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A CFG allows multiple sub-networks within S
Here the sub-networks are NP and VP

• S

NP
VP
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Transitioning between S and NP
Start
NP
VP
S
End
Adj
NP
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Transitioning between S and VP
VP

• S

NP
Vt
VP
VP2
NP
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Representing the network for The girl slept.
vi
VP
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The Grammar for The girl slept.

• Grammar
• S network
• initial(s,1).
• final(s,3).
• arc(s,1,np,2).
• arc(s,2,vp,3).
• NP network
• initial(np,1).
• final(np,3).
• arc(np,1,det,2).
• arc(np,2,n,3).
• VP network
• initial(vp,1).
• final(vp,2).
• arc(vp,1,vi,2).

• Lexicon
• word(the,det).
• word(girl,n).
• word(slept,vi).
• in the S network, there is
• an arc from state 1 to state 2
• labeled np.
• wksht 1.1
  

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Recursion is possible when arc labels refer to
other networks
PP
PP
Det
N

• NP

jump
P
NP
PP
The fish PPin NPthe pond PPin NPthe
mountains wksht 1.2
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CFG Processing
When the parser finishes processing the NP, it
pops back up to S2.

• S

NP
VP
How does the parser know how to do this?
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Keeping track of where you are

• A stack keeps track of where the processor should
  pop back to after successfully traversing a
  sub-network
• When moving to a sub-network, the processor
  pushes the network node to return to onto the
  stack
• When finished with the sub-network, the processor
  pops the network node from the stack

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Computer Simulation of this holding process

• String State Stack Comment
• The girl slept S1 --- Push to NP-network
• The girl slept NP1 S2 Recognize Det
• girl slept NP2 S2 Recognize N
• slept NP3 S2 Pop to S-network
• slept S2 --- Push to VP-network
• slept VP1 S3 Recognize V
• --- VP2 S3 Pop to S-network
• --- S3 success

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Complications with CFGs
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Agreementcauses the grammar to expand
considerably

• S ? npsg vpsg.
• S ? nppl vppl.
• Npsg ? detsg nsg.
• NPpl ? detpl npl.
• VPsg ? visg.
• VPpl ? vipl.

• arc(np,2,n,3). becomes
• arc(np,2,nsg,3)
• arc(np,2,npl,3).
• arc(vp,1,vi,2). becomes
• arc(vp,1,visg,2).
• arc(vp,1,vipl,2).

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Subcategorization also causes expansion

• VP ?vi.
• VP ? vt np.
• VP ? vl np.
• VP ? vl adjp.
• VP ? v2t.
• . . .
• . . .
• . . .

• arc(vp,1,vi,2).
• arc(vp,1,vt,2, np,3).
• arc(vp,1,vl,2,np,3).
• arc(vp,1,vl,2,adj,3).
• arc(vp,1,v2t,np,3,np,4).
• . . .
• . . .
• . . . COMLEX Manual

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Auxiliaries

• Word order is not a problem
• might have been being bothered
• Selection is a problem with the same consequences
  as agreement and subcat
• have seen
• have seeing