Homework & NLTK. CS 181: Natural Language Processing Lecture 9: Context Free Grammars. Motivation. Formal Def of CFG. Uses of CFG.
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1 C 181: Natural Language Processing Lecture 9: Context Free Grammars Kim Bruce Pomona College pring 2008 Homework & NLTK Review MLE, Laplace, and Good-Turing in smoothing.py Disclaimer: lide contents borrowed from many sources on web! 1 2 Motivation Formal Def of CFG Chunks of sentences behave as units Want to recover from input. Reason: Chunks are basis of meaning ubtrees of parse trees will represent meaningful chunks for us. G = <T, N,, R>, where T is a set of terminals (lexicon) N is a set of non-terminals. In linguistics, often also identify P! N, preterminals, which always rewrite as terminals. " N is start state. R is set of rules of form X #!, where X is nonterminal and! is sequence composed of terminals and non-terminals. L(G) = {w " T* #* w } 3 4 Uses of CFG Generate sentences of language Recognize sentences of language Impose structure as well! entences in language said to be grammatical Example CFG T = {this, that, a, the, man, book, flight, meal, include, read, does} N = {,,,, Det, Noun, Verb, Aux} - start R = # # Verb # Aux # Verb # Det # that this a the # Det Noun # book flight meal man # Noun Verb # book include read # Noun Aux # does 5 6
2 Derivation Parse Tree!! Det! The! The Noun! The man! The man Verb! The man read! The man read Det! The man read this! The man read this Noun! The man read this book Det The Noun man Verb read Det this Many derivations give the same tree. Abstracts away order! book 7 8 CFG s & Recursion Polymorphism Non-trivial recursion represented nicely with cfg s: # PP PP # Prep [ [ The student] [ [ VB took] [ a class [ PP in [ Edmunds]]] [ PP with [ her friend]]]] bracket notation represents tree Rule like # V allows to ignore internal complexity of. # and John liked Mary and she liked him # and John like Mary and uzy # and... Need X # X and X Any restrictions? 9 10 Unwanted Complexity ubcategorization Agreement He plays on the swings. They play on the swings.... this flight... these flights Other languages require gender ubject vs. object (he vs. him) Verbs with objects and indirect objects John sneezed. Mary found [ a phone]. Jane gave [ the teacher] [ an apple]. I prefer [ TO_ to do it myself] I was told [ it is not allowed to litter]. ubcategorization expresses constraints on a word on the number and type of arguments associated with it
3 Allows Incorrect entences # V Allows John sneezed the book. Distinguish between transitive & non-transitive but many more distinctions! ubcategorization frames Can complicate the grammar or add other mechanisms (non-cfg) to take care of these issues. Come back to it later! Movement [ [ My travel agent][ booked [ the flight]]] [ [ Which flight] do you want me to have the travel agent [V book]]? eparated object (the flight) from verb (book) How can we recover constituents? Equivalence of Grammars Normal Forms Two grammars are: strongly equivalent if they generate the same sentences they assign the same structure to each sentence weakly equivalent if they generate the same sentences they may not assign the same structure to each sentence Alas, weakly equivalent is undecidable! Useful in performing algorithms on cfg s Greibach Chomsky (CNF) Productions of form: A # B C or A # a or # " Theorem: Any cfg can be converted into a weakly equivalent grammar in CNF Conversion to CNF MAKE NON-RECURIVE Make non-recursive (add if necessary) Only necessary if " is in language.. Eliminate all "-moves except for Eliminate unit productions ( # T). Reduce right hand sides to length 2. Convert all terminals on rt sides to nonterminals Remove any useless rules & symbols Convert: # " # A B A # " tep 1: # " # # A B # " A # " 17 18
4 Eliminate "-moves tep 1: # " # # A B # " A # " tep 2: # " # # A B # A B # B # B tep 2: # " # Eliminate Unit Productions # A B # A B # B # B tep 3: # " # A B # A B # B # w B # v # A B # A B # B # w B # v hrink RH Eliminate terminals tep 3: # " # A B # A B # B # w B # v # A B # A B # B # w B # v tep 4: # " # A P P # B # A B # B # w B # v # A P # A B # B # w B # v A # x Q Q # y z tep 4: # " # A P P # B # A B # B # w B # v # A P # A B # B # w B # v A # x Q Q # y z tep 5: # " # A P P # B # A B # B # W B # v # A P # A B # B # W B # v A # X Q Q # Y Z B # W B W # w X # x Y # y Z # z Parsing Parsing CFG s Assign parse trees to legal sentence of the language. Regular languages (expressions) can be recognized by FA in linear time. Can t represent languages like a n b n. Cfg s can t represent a n b n c n. Requires context-sensitive. Requires push-down automaton. FA w/ stack to hold partial results Complexity space to parse - O(n) (proportional to recursion), time O(n 3 ) 23 24
5 Parsing Empty Rules and Left Recursion Recognizer just says yes or no Parser: Given term, find parse tree Bottom-up Top-down Want to find all parse trees! Ambiguity! Want to determine which is most likely hort-term memory in humans is limited Grammars can have an "-rule: A # " have left-recursive rules: A # AB E.g. # PP Make parsing more difficult! Top-Down Parsing Top-Down Parsing Hypothesis-Driven Parsing Goal-directed tart with and get to string, w. Can use depth-first or breadth-first search # # Aux # # Det # Noun # Noun # Verb # Verb Det # that this a the Noun # book flight meal man Verb # book include read Aux # does Parse: Book that flight Aux Det Verb Det Verb Verb Verb Verb Probs w/top-down Left recursive rules, e.g. # PP lead to infinite recursion. Inefficient if lots of rules w/ same LH Useless work: Expands trees that have no evidence. Do well if search directed by grammar. Treat pre-terminals before start parse. book Det 29 30
6 Bottom-Up Parsing Data-driven: tart w/ string. Rewrite by replacing RH by LH of rules until get. May have several RH matches. Usually presented as shift-reduce parse Noun Det Noun Verb Det Noun Noun Det Noun Verb Det Noun sentence # NounPhrase VerbPhrase NounPhrase # Art Noun VerbPhrase # Verb Adverb Verb Art # the a... Verb # jumps sings... Noun # dog cat... hift-reduce Parse: The dog jumps Draw trees as parse! tack Input equence () (the dog jumps) (the) (dog jumps) HIFT word onto stack (Art) (dog jumps) REDUCE using grammar rule (Art dog) (jumps) HIFT.. (Art Noun) (jumps) REDUCE.. (NounPhrase) (jumps) REDUCE (NounPhrase jumps) () HIFT (NounPhrase Verb) () REDUCE (NounPhrase VerbPhrase)() REDUCE (entence) () UCCE Bottom-Up Parsing Do we shift or reduce? If reduce, which rule do we use? With prog. langs, build table to always tell you what to do -- deterministic. Programming languages designed to be unambiguous. We don t have that luxury! "-rules can be applied anywhere! May need to backtrack! Top-Down vs. Bottom-Up Keys to uccess Top-down may explore paths that can never result in desired string In prog. langs, can make sure that doesn t happen. Bottom up may build subtrees that can not be part of trees rooted at. Both may have to repeat work when backtracking! Watch out for bad grammars left-recursive for top-down ( # PP) Try to avoid redoing work when backtracking Grammar transformations help... but linguists will hate you! 35 36
7 Dynamic Programming Next time: CYK Earley s Algorithm Chart parsing Probabilistic versions Any Questions? 37 38
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