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Context Free Grammars Reading: Chap 12-13, Jurafsky & Martin This slide set was adapted from J. Martin, U. Colorado PowerPoint Presentation
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Context Free Grammars Reading: Chap 12-13, Jurafsky & Martin This slide set was adapted from J. Martin, U. Colorado Instructor: Rada Mihalcea. Syntax. Syntax = rules describing how words can connect to each other * that and after year last I saw you yesterday

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slide1

Context Free

Grammars

Reading: Chap 12-13, Jurafsky & Martin

This slide set was adapted from J. Martin, U. Colorado

Instructor: Rada Mihalcea

syntax
Syntax
  • Syntax = rules describing how words can connect to each other
  • * that and after year last
  • I saw you yesterday
  • colorless green ideas sleep furiously
  • the kind of implicit knowledge of your native language that you had mastered by the time you were 3 or 4 years old without explicit instruction
  • not necessarily the type of rules you were later taught in school.
syntax3
Syntax
  • Why should you care?
    • Grammar checkers
    • Question answering
    • Information extraction
    • Machine translation
context free grammars
Context-Free Grammars
  • Capture constituency and ordering
    • Ordering
      • What are the rules that govern the ordering of words and bigger units in the language
    • Constituency
    • How do words group into units and what we say about how the various kinds of units behave
cfg examples
CFG Examples
  • S -> NP VP
  • NP -> Det NOMINAL
  • NOMINAL -> Noun
  • VP -> Verb
  • Det -> a
  • Noun -> flight
  • Verb -> left
  • these rules are defined independent of the context
  • where they might occur -> CFG
slide6
CFGs
  • 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
  • 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
parsing
Parsing
  • Parsing is the process of taking a string and a grammar and returning a (many?) parse tree(s) for that string
  • Other options
  • Regular languages (expressions)
    • Too weak
  • Context-sensitive
    • Too powerful
context
Context?
  • The notion of context in CFGs is not the same as the ordinary meaning of the word context in language.
  • All it really means is that the non-terminal on the left-hand side of a rule is out there all by itself
    • A -> B C
    • Means that I can rewrite an A as a B followed by a C regardless of the context in which A is found
key constituents english
Key Constituents (English)
  • Sentences
    • Noun phrases
    • Verb phrases
    • Prepositional phrases
sentence types
Sentence-Types
  • Declaratives: A plane left
    • S -> NP VP
  • Imperatives: Leave!
    • S -> VP
  • Yes-No Questions: Did the plane leave?
    • S -> Aux NP VP
  • WH Questions: When did the plane leave?
    • S -> WH Aux NP VP
conjunctive constructions
Conjunctive Constructions
  • S -> S and S
    • John went to NY and Mary followed him
  • NP -> NP and NP
  • VP -> VP and VP
  • In fact the right rule for English is
    • X -> X and X
recursion
Recursion
  • We’ll have to deal with rules such as the following where the non-terminal on the left also appears somewhere on the right (directly).
    • NP -> NP PP [[The flight] [to Boston]]
    • VP -> VP PP [[departed Miami] [at noon]]
recursion13
Recursion
  • Of course, this is what makes syntax interesting
    • 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
the point
The Point
  • 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 point15
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
potential problems in cfg
Potential Problems in CFG
  • Agreement
  • Subcategorization
  • Movement
agreement
*This dogs

*Those dog

*This dog eat

*Those dogs eats

Agreement
  • This dog
  • Those dogs
  • This dog eats
  • Those dogs eat
subcategorization
Subcategorization
  • Sneeze: John sneezed
  • Find: Please find [a flight to NY]NP
  • Give: Give [me]NP[a cheaper fare]NP
  • Help: Can you help [me]NP[with a flight]PP
  • Prefer: I prefer [to leave earlier]TO-VP
  • Told: I was told [United has a flight]S
  • *John sneezed the book
  • *I prefer United has a flight
  • *Give with a flight
  • Subcat expresses the constraints that a predicate (verb for now) places on the number and type of the argument it wants to take
slide19
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
    • Subcategorization frames can fix this problem (“slow down” overgeneration)
movement
Movement
  • Core example
    • [[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.
movement21
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 its separated from its verb by 2 other verbs.
formally
Formally…
  • To put all previous discussions/examples in a formal definition for CFG:
  • A context free grammar has four parameters:
  • A set of non-terminal symbols N
  • A set of terminal symbols T
  • A set of production rules P, each of the form A  a, where A is a non-terminal, and a is a string of symbols from the infinite set of strings (T  N)*
  • A designated start symbol S
grammar equivalence and normal form
Grammar equivalence and normal form
  • Strong equivalence:
    • two grammars are strongly equivalent if:
      • they generate the same set of strings
      • they assign the same phrase structure to each sentence
    • two grammars are weakly equivalent if:
      • they generate the same set of strings
      • they do not assign the same phrase structure to each sentence
  • Normal form
    • Restrict the form of productions
    • Chomsky Normal Form (CNF)
    • Right hand side of the productions has either one or two terminals or non-terminals
    • e.g. A -> BC A -> a
    • Any grammar can be translated into a weakly equivalent CNF
    • A -> B C D <=> A-> B X X -> C D
building tree structures
Building tree structures
  • Draw tree structures for the following phrases
  • Dallas
  • from Denver
  • arriving in Washington
  • I need to fly between Philadelphia and Atlanta