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Computational Linguistics Introduction

Computational Linguistics Introduction. Context Free Grammars. Chomsky Hierarchy. Context Free Grammars (CFGs). Sets of rules expressing how symbols of the language fit together, e.g. S -> NP VP NP -> Det N Det -> the N -> dog. What Does Context Free Mean?.

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Computational Linguistics Introduction

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  1. Computational Linguistics Introduction Context Free Grammars CLINT-LN CFG

  2. Chomsky Hierarchy CLINT-LN CFG

  3. Context Free Grammars (CFGs) Sets of rules expressing how symbols of the language fit together, e.g.S -> NP VPNP -> Det NDet -> theN -> dog CLINT-LN CFG

  4. What Does Context Free Mean? • LHS of rule is just one symbol. • Can haveNP -> Det N • Cannot haveX NP Y -> X Det N Y • Everyday examples of context sensitivity CLINT-LN CFG

  5. What Does Context Free Mean? • LHS of rule is just one symbol. • Can haveNP -> Det N • Cannot haveX NP Y -> X Det N Y • Everyday examples of context sensitivityy e -> i e[b]# -> [p]# CLINT-LN CFG

  6. Grammar Symbols • Non Terminal Symbols • Terminal Symbols • Words • Preterminals CLINT-LN CFG

  7. Non Terminal Symbols • Symbols which have definitions • Symbols which appear on the LHS of rulesS-> NP VPNP -> Det NDet -> theN-> dog CLINT-LN CFG

  8. Non Terminal Symbols • Same Non Terminals can have several definitionsS-> NP VPNP -> Det N NP -> N Det -> theN-> dog CLINT-LN CFG

  9. TerminalSymbols • Symbols which appear in final string • Correspond to words • Are not defined by the grammar S -> NP VPNP -> Det NDet -> theN -> dog CLINT-LN CFG

  10. Parts of Speech (POS) • NT Symbols which produce terminal symbols are sometimes called pre-terminals S -> NP VPNP -> Det NDet -> theN-> dog • Sometimes we are interested in the shape of sentences formed from pre-terminalsDet N VAux N V D N CLINT-LN CFG

  11. CFG - formal definition A CFG is a tuple (N,,R,S) • N is a set of non-terminal symbols •  is a set of terminal symbols disjoint from N • R is a set of rules each of the form A   where A is non-terminal • S is a designated start-symbol CLINT-LN CFG

  12. grammar: S  NP VP NP  N VP  V NP lexicon: V  kicks N  John N  Bill N = {S, NP, VP, N, V}  = {kicks, John, Bill} R = (see opposite) S = “S” CFG - Example CLINT-LN CFG

  13. Class Exercise • Write grammars that generate the following languages, for m > 0 (ab)m anbm anbn • Which of these are Regular? • Which of these are Context Free? CLINT-LN CFG

  14. (ab)m for m > 0 S -> a b S -> a b S CLINT-LN CFG

  15. (ab)m for m > 0 S -> a b S -> a b S S -> a X X -> b Y Y -> a b Y -> S CLINT-LN CFG

  16. S -> A B A -> a A -> a A B -> b B -> b B anbm CLINT-LN CFG

  17. S -> A B A -> a A -> a A B -> b B -> b B S -> a AB AB -> a AB AB -> B B -> b B -> b B anbm CLINT-LN CFG

  18. NP VP N V NP N John kicks Bill Grammar Defines a Structure grammar: S  NP VP NP  N VP  V NP lexicon: V  kicks N  John N  Bill S CLINT-LN CFG

  19. NP N Bill Different Grammar Different Stucture grammar: S  NP NP NP  N V NP  N lexicon: V  kicks N  John N  Bill S NP N V John kicks CLINT-LN CFG

  20. Which Grammar is Best? • The structure assigned by the grammar should be appropriate. • The structure should • Be understandable • Allow us to make generalisations. • Reflect the underlying meaning of the sentence. CLINT-LN CFG

  21. Ambiguity • A grammar is ambiguous if it assigns two or more structures to the same sentence. NP  NP CONJ NP NP  N lexicon: CONJ  and N  John N  Bill • The grammar should not generate too many possible structures for the same sentence. CLINT-LN CFG

  22. Criteria for Evaluating Grammars • Does it undergenerate? • Does it overgenerate? • Does it assign appropriate structures to sentences it generates? • Is it simple to understand? How many rules are there? • Does it contain just a few generalisations or is it full of special cases? • How ambiguous is it? How many structures does it assign for a given sentence? CLINT-LN CFG

  23. PATR-II • The PATR-II formalism can be viewed as a computer language for encoding linguistic information. • A PATR-II grammar consists of a set of rules and a lexicon. • The rules are CFG rules augmented with constaints. • The lexicon provides information about terminal symbols. CLINT-LN CFG

  24. Grammar (grammar.grm) Rule s -> np vp Rule np -> n Rule vp -> v Lexicon (lexicon.lex) \w uther \c n \w sleeps \c v Example PATR-IIGrammar and Lexicon CLINT-LN CFG

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