Natural Language Processing CSCI 4152/6509 Lecture 26 CFGs and CYK - - PowerPoint PPT Presentation

Natural Language Processing CSCI 4152/6509 — Lecture 26 CFGs and CYK Parsing Algorithm

Instructor: Vlado Keselj Time and date: 09:35–10:25, 12-Mar-2020 Location: Dunn 135

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Previous Lecture

HMM POS-tagging with a product-sum algorithm Part IV: Parsing (Syntactic Processing) Natural language syntax:

◮ phrase structure, clauses, sentences

Reading: [JM] Ch 12 Parsing, parse tree examples

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Some Notions about CFGs

CFG, also known as Phrase-Structure Grammar (PSG) Equivalent to BNF (Backus-Naur form) Idea from Wundt (1900), formally defined by Chomsky (1956) and Backus (1959) Typical notation (V, T, P, S); also (N, Σ, R, S) Direct derivation, derivation Example of a direct derivation: S ⇒ NP VP Example of a derivation (beginning of): S ⇒ NP VP ⇒ DT NN VP ⇒ That NN VP ⇒ . . . Left-most and right-most derivation

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Parse Tree Example (revisited)

DT NN VBD DT NN IN DT That man caught the butterfly with a NN net. NP NP NP PP VP S

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Leftmost Derivation Example

S ⇒ NP VP ⇒ DT NN VP ⇒ That NN VP ⇒ That manVP ⇒ That man VBD NP PP ⇒ That man caught NP PP ⇒ That man caught DT NN PP ⇒ That man caught the NN PP ⇒ That man caught the butterfly PP ⇒ That man caught the butterfly IN NP ⇒ That man caught the butterfly with NP ⇒ That man caught the butterfly with DT NN ⇒ That man caught the butterfly with a NN ⇒ That man caught the butterfly with a net

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Some Notions about CFGs (continued)

Language generated by a CFG Context-Free languages Parsing task Ambiguous sentences Ambiguous grammars Inherently ambiguous languages

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Bracket Representation of a Parse Tree

(S (NP (DT That) (NN man)) (VP (VBD caught) (NP (DT the) (NN butterfly)) (PP (IN with) (NP (DT a) (NN net) ) ) ) )

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Some Notes on CFGs

Left-hand side (lhs) and right-had side (rhs) of a production S

• lhs

→ NP VP

rhs

Empty rule (epsilon rule, epsilon production): V → ǫ Unit production: A → B, where A and B are non-terminals Notational variations:

◮ use of ‘|’: P → N | A P, instead of P → N, P → A P ◮ BNF notation: P ::= N | A P ◮ use of word ‘opt’: NP ::= DT NN PPopt ◮ or Kleene star: NP ::= DT NN PP∗ CSCI 4152/6509, Vlado Keselj Lecture 26 8 / 12

CYK Chart Parsing Algorithm

When parsing NLP, there are generally two approaches:

1

Backtracking to find all parse trees

2

Chart parsing

CYK algorithm: a simple chart parsing algorithm CYK: Cocke-Younger-Kasami algorithm CYK can be applied only to a CNF grammar

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Chomsky Normal Form

all rules are in one of the forms:

1

A → B C, where A, B, and C are nonterminals, or

2

A → w, where A is a nonterminal and w is a terminal

If a grammar is not in CNF, it can be converted to it

Is the following grammar in CNF? S → NP VP VP → V NP N → time V → like NP → N VP → V PP N → arrow V → flies NP → N N PP → P NP N → flies P → like NP → D N D → an

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How about this grammar? (Is it in CNF?) S → NP VP VP → V NP N → time V → like NP → time VP → V PP N → arrow V → flies NP → N N PP → P NP N → flies P → like NP → D N D → an

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CYK Example

The following grammar in CNF is given: S → NP VP VP → V NP N → time V → like NP → time VP → V PP N → arrow V → flies NP → N N PP → P NP N → flies P → like NP → D N D → an

1 2 3 4 5

time flies like arrow an

NP,N V, N V, P D N NP NP PP, VP VP S CSCI 4152/6509, Vlado Keselj Lecture 26 12 / 12