Context Free Grammars. Many slides from Michael Collins

Transcription

1 Context Free Grammars Many slides from Michael Collins

2 Overview I An introduction to the parsing problem I Context free grammars I A brief(!) sketch of the syntax of English I Examples of ambiguous structures

3 Parsing (yntactic tructure) IUT: OUTPUT: Boeing is located in eattle. N V Boeing is V PP located P in N eattle

4 yntactic Formalisms I Work in formal syntax goes back to Chomsky s PhD thesis in the 1950s I Examples of current formalisms: minimalism, lexical functional grammar (LFG), head-driven phrase-structure grammar (HPG), tree adjoining grammars (TAG), categorial grammars

5 Data for Parsing Experiments I Penn WJ Treebank = 50,000 sentences with associated trees I Usual set-up: 40,000 training sentences, 2400 test sentences An example tree: TOP N N VBD PP PP AD IN CD NN IN RB PP QP PRP$ JJ NN CC JJ NN NN IN $ CD CD PUNC, BAR N PUNC, WHAD WRB DT NN VBZ QP NN PUNC. RB CD Canadian Utilities had 1988 revenue of C$ 1.16 billion, mainly from its natural gas and electric utility businessesin Alberta, where the company serves about 800,000 customers.

6 The Information Conveyed by Parse Trees (1) Part of speech for each word (N = noun, V = verb, DT = determiner) DT N V the burglar robbed DT N the apartment

7 The Information Conveyed by Parse Trees (continued) (2) Phrases DT N V the burglar robbed DT N the apartment Noun Phrases (): the burglar, the apartment Verb Phrases (): robbed the apartment entences (): the burglar robbed the apartment

8 The Information Conveyed by Parse Trees (continued) (3) Useful Relationships subject V verb DT N V the burglar robbed DT N ) the burglar is the subject of robbed the apartment

9 An Example Application: Machine Translation I English word order is I Japanese word order is subject verb object subject object verb English: Japanese: English: Japanese: IBM bought Lotus IBM Lotus bought ources said that IBM bought Lotus yesterday ources yesterday IBM Lotus bought that said

10 -A ources, BAR-A, VB said COMP that yesterday -A IBM -A, VB Lotus bought

11 Overview I An introduction to the parsing problem I Context free grammars I A brief(!) sketch of the syntax of English I Examples of ambiguous structures

12 Context-Free Grammars Hopcroft and Ullman, 1979 A context free grammar G =(N,,R,) where: I N is a set of non-terminal symbols I is a set of terminal symbols I R is a set of rules of the form X! Y 1 Y 2...Y n for n 0, X 2 N, Y i 2 (N [ ) I 2 N is a distinguished start symbol

13 A Context-Free Grammar for English N = {,,, PP, DT, Vi, Vt, NN, IN} = = {sleeps, saw, man, woman, telescope, the, with, in} R =!! Vi! Vt! PP! DT NN! PP PP! IN Vi! sleeps Vt! saw NN! man NN! woman NN! telescope DT! the IN! with IN! in Note: =sentence, =verb phrase, =noun phrase, PP=prepositional phrase, DT=determiner, Vi=intransitive verb, Vt=transitive verb, NN=noun, IN=preposition

14 Left-Most Derivations A left-most derivation is a sequence of strings s 1...s n, where I s 1 =, the start symbol I s n 2, i.e. s n is made up of terminal symbols only I Each s i for i =2...n is derived from s i 1 by picking the left-most non-terminal X in s i 1 and replacing it by some where X! is a rule in R For example: [], [ ], [D N ], [the N ], [the man ], [the man Vi], [the man sleeps] Representation of a derivation as a tree: D the N man Vi sleeps

15 An Example DERIVATION RULE UED

16 An Example DERIVATION RULE UED!

17 An Example DERIVATION DT N RULE UED!! DT N

18 An Example DERIVATION DT N the N RULE UED!! DT N DT! the

19 An Example DERIVATION DT N the N the dog RULE UED!! DT N DT! the N! dog

20 An Example DERIVATION DT N the N the dog the dog VB RULE UED!! DT N DT! the N! dog! VB

21 An Example DERIVATION DT N the N the dog the dog VB the dog laughs RULE UED!! DT N DT! the N! dog! VB VB! laughs

22 An Example DERIVATION DT N the N the dog the dog VB the dog laughs RULE UED!! DT N DT! the N! dog! VB VB! laughs DT N the dog VB laughs

23 Properties of CFGs I A CFG defines a set of possible derivations I A string s 2 is in the language defined by the CFG if there is at least one derivation that yields s I Each string in the language generated by the CFG may have more than one derivation ( ambiguity )

24 An Example of Ambiguity he PP VB PP IN drove IN down DT NN in DT the NN car the street

25 An Example of Ambiguity (continued) he VB PP drove IN down PP DT NN IN the street in DT NN the car

26 The Problem with Parsing: Ambiguity IUT: he announced a program to promote safety in trucks and vans POIBLE OUTPUT: + he he he he announced he announced announced he announced a program announced a program announced PP to promote safety PP a program to promote safety in PP a program in trucks and vans in to promote trucks and vans to promote safety trucks and vans and vans and and vans a program safety PP in vans a program to promote PP to promote trucks safety in safety PP trucks in trucks And there are more...

27 Overview I An introduction to the parsing problem I Context free grammars I A brief(!) sketch of the syntax of English I Examples of ambiguous structures

28 Product Details (from Amazon) Hardcover: 1779 pages Publisher: Longman; 2nd Revised edition Language: English IBN-10: IBN-13: Product Dimensions: 8.4 x 2.4 x 10 inches hipping Weight: 4.6 pounds

29 A Brief Overview of English yntax Parts of peech (tags from the Brown corpus): I Nouns NN = singular noun e.g., man, dog, park NN = plural noun e.g., telescopes, houses, buildings N = proper noun e.g., mith, Gates, IBM I Determiners DT = determiner e.g., the, a, some, every I Adjectives JJ = adjective e.g., red, green, large, idealistic

30 AFragmentofaNounPhraseGrammar N ) NN N ) NN N N ) JJ N N ) N N ) DT N NN ) box NN ) car NN ) mechanic NN ) pigeon DT ) the DT ) a JJ ) fast JJ ) metal JJ ) idealistic JJ ) clay

31 Prepositions, and Prepositional Phrases I Prepositions IN = preposition e.g., of, in, out, beside, as

32 An Extended Grammar N ) NN N ) NN N N ) JJ N N ) N N ) DT N PP ) IN N ) N PP NN ) box NN ) car NN ) mechanic NN ) pigeon DT ) the DT ) a JJ ) fast JJ ) metal JJ ) idealistic JJ ) clay IN ) in IN ) under IN ) of IN ) on IN ) with IN ) as Generates: in a box, under the box, the fast car mechanic under the pigeon in the box,...

33 Verbs, Verb Phrases, and entences I Basic Verb Types Vi = Intransitive verb Vt = Transitive verb Vd = Ditransitive verb e.g., sleeps, walks, laughs e.g., sees, saw, likes e.g., gave I Basic Rules! Vi! Vt! Vd I Basic Rule! Examples of : sleeps, walks, likes the mechanic, gave the mechanic the fast car Examples of : the man sleeps, the dog walks, the dog gave the mechanic the fast car

34 PPs Modifying Verb Phrases Anewrule:! PP New examples of : sleeps in the car, walks like the mechanic, gave the mechanic the fast car on Tuesday,...

35 Complementizers, and BARs I Complementizers COMP = complementizer e.g., that I BAR ubordinate clause BAR! COMP Examples: that the man sleeps, that the mechanic saw the dog...

36 More Verbs I New Verb Types V[5] e.g., said, reported V[6] e.g., told, informed V[7] e.g., bet I New Rules! V[5] BAR! V[6] BAR! V[7] BAR Examples of New s: said that the man sleeps told the dog that the mechanic likes the pigeon bet the pigeon $50 that the mechanic owns a fast car

37 Coordination I A New Part-of-peech: CC = Coordinator e.g., and, or, but I New Rules! CC N! N CC N! CC! CC BAR! BAR CC BAR

38 We ve Only cratched the urface... I Agreement The dogs laugh vs. The dog laughs I Wh-movement Long- distance dependency The dog that the cat liked I Active vs. passive The dog saw the cat vs. The cat was seen by the dog I If you re interested in reading more: yntactic Theory: A Formal Introduction, 2nd Edition. Ivan A. ag, Thomas Wasow, and Emily M. Bender.

39 Overview I An introduction to the parsing problem I Context free grammars I A brief(!) sketch of the syntax of English I Examples of ambiguous structures

40 ources of Ambiguity I Part-of-peech ambiguity NN! duck Vi! duck PP PP Vt IN V IN saw PRP NN with the telescope saw with the telescope her duck her Vi duck

41 I PP Vi PP IN drove IN down DT NN in DT the NN car the road

42 I Vi PP drove IN down PP DT NN IN the road in DT NN the car

43 Two analyses for: John was believed to have been shot by Bill With the same set of grammar rules

44 ources of Ambiguity: Noun Premodifiers I Noun premodifiers: D N D N the JJ N the N N fast NN N JJ N NN car NN fast NN mechanic mechanic car