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ELABORAZIONE DEL
LINGUAGGIO NATURALE
SINTASSI: GRAMMATICHE CONTEXTFREE
Syntax
• Syntax: from Greek syntaxis “setting out together,
arrangement’’
• Refers to the way words are arranged together,
and the relationship between them.
• Distinction:
– Prescriptive grammar: how people ought to talk
– Descriptive grammar: how they do talk
• Goal of syntax is to model the knowledge of that
people unconsciously have about the grammar of
their native language
key ideas of syntax
• Constituency
• Subcategorization
• Grammatical relations
Plus one part we won’t have time for:
• Movement/long-distance dependency
Context-Free Grammars (CFG)
• Capture constituency and ordering
– Ordering:
• What are the rules that govern the ordering of words
and bigger units in the language?
– Constituency:
How words group into units and how the various
kinds of units behave
Constituency
• E.g., Noun phrases (NPs)
•
•
•
•
•
•
Three parties from Brooklyn
A high-class spot such as Mindy’s
The Broadway coppers
They
Harry the Horse
The reason he comes into the Hot Box
• How do we know these form a constituent?
Constituency (II)
– They can all appear before a verb:
•
•
•
•
Three parties from Brooklyn arrive…
A high-class spot such as Mindy’s attracts…
The Broadway coppers love…
They sit
– But individual words can’t always appear before verbs:
•
•
•
•
*from arrive…
*as attracts…
*the is
*spot is…
– Must be able to state generalizations like:
• Noun phrases occur before verbs
Constituency (III)
• Preposing and postposing:
– On September 17th, I’d like to fly from Atlanta to Denver
– I’d like to fly on September 17th from Atlanta to Denver
– I’d like to fly from Atlanta to Denver on September 17th.
• But not:
– *On September, I’d like to fly 17th from Atlanta to Denver
– *On I’d like to fly September 17th from Atlanta to Denver
Indicating constituents: brackets, trees
• [S [NP [PRO I]] [VP [V prefer] [NP [Det a] [Nom [N morning]
[N flight] ] ] ] ]
S
NP
VP
NP
Nom
Pro Verb
I
prefer
Det
a
Noun
morning
Noun
flight
Beyond regular languages: ContextFree Grammars
S  NP VP
NP  Det Nominal
Nominal  Noun
VP  V
Det  the
Det  a
Noun  flight
V  left
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CFGs: set of rules
• S -> NP VP
– This says that there are units called S, NP, and VP
in this language
– That an S consists of an NP followed immediately
by a VP
– Doesn’t say that that’s the only kind of S
– Nor does it say that this is the only place that NPs
and VPs occur
Generativity
• As with FSAs you can view these rules as
either analysis or synthesis machines
– Generate strings in the language
– Reject strings not in the language
– Impose structures (trees) on strings in the
language
• How can we define grammatical vs.
ungrammatical sentences?
Derivations
• A derivation is a sequence of rules applied to a
string that accounts for that string
– Covers all the elements in the string
– Covers only the elements in the string
Derivations as Trees
S
NP
VP
NP
Nom
Pro Verb
I
prefer
Det
a
Noun
morning
Noun
flight
CFGs more formally
•
A context-free grammar has 4 parameters
(“is a 4-tuple”)
1) A set of non-terminal symbols (“variables”) N
2) A set of terminal symbols  (disjoint from N)
3) A set of productions P, each of the form
•
•
A -> 
Where A is a non-terminal and  is a string of symbols from the
infinite set of strings (  N)*
4) A designated start symbol S
Defining a CF language via derivation
•
A string A derives a string B if
–
•
A can be rewritten as B via some series of rule applications
More formally:
–
–
–
If A ->  is a production of P
 and  are any strings in the set (  N)*
Then we say that
•
–
–
Derivation is a generalization of direct derivation
Let 1, 2, … m be strings in (  N)*, m>= 1, s.t.
•
•
–
A directly derives  or A  
1 2, 2 3… m-1 m
We say that 1derives m or 1* m
We then formally define language LG generated by grammar G
•
•
A set of strings composed of terminal symbols derived from S
LG = {w | w is in * and S * w}
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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NPs
• NP -> Pronoun
– I came, you saw it, they conquered
• NP -> Proper-Noun
– Los Angeles is west of Texas
– John Hennessy is the president of Stanford
• NP -> Det Noun
– The president
• NP -> Nominal
• Nominal -> Noun Noun
– A morning flight to Denver
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
NLE
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Types of postnominal modifiers
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PPs
• PP -> Preposition NP
– From LA
– To the store
– On Tuesday morning
– With lunch
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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Recursion
[[Flights] [from Denver]]
[[[Flights] [from Denver]] [to Miami]]
[[[[Flights] [from Denver]] [to Miami]] [in February]]
[[[[[Flights] [from Denver]] [to Miami]] [in February]] [on a
Friday]]
Etc.
NP -> NP PP
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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Implications of recursion and contextfreeness
• If you have a rule like
– VP -> V NP
– It only cares that the thing after the verb is an NP
It doesn’t have to know about the internal affairs
of that NP
The point
•
•
VP -> V NP
(I) hate
flights from Denver
flights from Denver to Miami
flights from Denver to Miami in February
flights from Denver to Miami in February on a Friday
flights from Denver to Miami in February on a Friday under $300
flights from Denver to Miami in February on a Friday under $300 with lunch
Problems
• Agreement
• Subcategorization
• Movement (for want of a better term)
Agreement
• This dog
• Those dogs
• *This dogs
• *Those dog
• This dog eats
• Those dogs eat
• *This dog eat
• *Those dogs eats
Possible CFG Solution
•
•
•
•
S -> NP VP
NP -> Det Nominal
VP -> V NP
…
•
•
•
•
•
•
•
SgS -> SgNP SgVP
PlS -> PlNp PlVP
SgNP -> SgDet SgNom
PlNP -> PlDet PlNom
PlVP -> PlV NP
SgVP ->SgV Np
…
CFG Solution for Agreement
• It works and stays within the power of CFGs
• But it’s ugly
• And it doesn’t scale all that well
Subcategorization
• Sneeze: John sneezed
• *John sneezed the book
• Say: You said [United has a flight]S
• Prefer: I prefer [to leave earlier]TO-VP
• *I prefer United has a flight
• Give: Give [me]NP[a cheaper fare]NP
• Help: Can you help [me]NP[with a flight]PP
• *Give with a flight
Subcategorization
• Subcat expresses the constraints that a
predicate (verb for now) places on the number
and syntactic types of arguments it wants to
take (occur with).
So?
• So the various rules for VPs overgenerate
– They permit the presence of strings containing verbs
and arguments that don’t go together
– For example:
– VP -> V NP
– therefore
Sneezed the book is a VP since “sneeze” is a verb and
“the book” is a valid NP
Possible CFG Solution
•
•
•
•
VP -> V
VP -> V NP
VP -> V NP PP
…
•
•
•
•
VP -> IntransV
VP -> TransV NP
VP -> TransVwPP NP PP
…
Forward Pointer
• It turns out that verb subcategorization facts
will provide a key element for semantic
analysis (determining who did what to who in
an event).
Movement
• Core example
– My travel agent booked the flight
– [[My travel agent]NP [booked [the flight]NP]VP]S
• i.e. “book” is a straightforward transitive verb. It
expects a single NP arg within the VP as an
argument, and a single NP arg as the subject.
Movement
• What about?
– Which flight do you want me to have the travel
agent book?
• The direct object argument to “book” isn’t
appearing in the right place. It is in fact a long
way from where its supposed to appear.
• And note that it’s separated from its verb by 2
other verbs.
CFGs: a summary
• CFGs appear to be just about what we need to account for a lot of basic
syntactic structure in English.
• But there are problems
– That can be dealt with adequately, although not elegantly, by staying within
the CFG framework.
• There are simpler, more elegant, solutions that take us out of the CFG
framework (beyond its formal power).
Syntactic theories: HPSG, LFG, CCG, Minimalism, etc.
Other syntactic stuff
• Grammatical relations
– Subject
• I booked a flight to New York
• The flight was booked by my agent
– Object
• I booked a flight to New York
– Complement
• I said that I wanted to leave
Dependency parsing
•
•
•
•
Word to word links instead of constituency
Based on the European rather than American traditions
But dates back to the Greeks
The original notions of Subject, Object and the progenitor of
subcategorization (called ‘valence’) came out of Dependency theory.
• Dependency parsing is quite popular as a computational model
since relationships between words are quite useful
Dependency parsing
S
VP
NP
PP
NP
IN
NNS
VBN
NP
NNS
CC
Parse tree:
VP
VBD
PP
NP
IN
NN
NNP
NNP
Bills on ports and immigration were submitted by Senator Brownback
Nesting of
multi-word
constituents
submitted
nsubjpass
Bills
prep_on
ports
agent
Typed dep parse:
Brownback
nn
Grammatical
relations between
individual words
auxpass
were
conj_and
immigration
Senator
Why are dependency parses useful?
• Example: multi-document summarization
Need to identify sentences from different
documents that each say roughly the same
thing:
phrase structure trees of paraphrasing
sentences which differ in word order can be
significantly different
but dependency representations will be very
similar
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/Contex
t-free%20language
– Wikipedia:
http://en.wikipedia.org/wiki/Contextfree_grammar
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ACKNOWLEDGMENTS
• Many of these slides borrowed from Jim
Martin