Basic parsing with context free grammars
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Basic Parsing with Context-Free Grammars. Analyzing Linguistic Units. Morphological parsing: analyze words into morphemes and affixes rule-based, FSAs, FSTs Ngrams for Language Modeling POS Tagging Syntactic parsing: identify constituents and their relationships

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Basic Parsing with Context-Free Grammars

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Basic Parsing with Context-Free Grammars

CS 4705


Analyzing Linguistic Units

  • Morphological parsing:

    • analyze words into morphemes and affixes

    • rule-based, FSAs, FSTs

  • Ngrams for Language Modeling

  • POS Tagging

  • Syntactic parsing:

    • identify constituents and their relationships

    • to see if a sentence is grammatical

    • to assign an abstract representation of meaning


Syntactic Parsing

  • Declarative formalisms like CFGs, FSAs define the legal strings of a language -- but only tell you ‘this is a legal string of the language X’

  • Parsing algorithms specify how to recognize the strings of a language and assign each string one (or more) syntactic analyses

  • Parsing useful for grammar checking, semantic analysis, MT, QA, information extraction, speech recognition…almost every task in NLP…but…


Parsing as a Form of Search

  • Searching FSAs

    • Finding the right path through the automaton

    • Search space defined by structure of FSA

  • Searching CFGs

    • Finding the right parse tree among all possible parse trees

    • Search space defined by the grammar

  • Constraints provided by the input sentence and the automaton or grammar


CFG for Fragment of English

LC’s

TopDBotUp

E.g.


Parse Tree for ‘Book that flight’ for Prior CFG

SVPNP NomVDet NBookthatflight


S  NP VP

VP  V

S  Aux NP VP

PP -> Prep NP

S  VP (1)

N  book | flight | meal | money

NP  Det Nom (3)

V  book | include | prefer

NP PropN

Aux  does

Nom  N Nom

Prep from | to | on

Nom  N (4)

PropN  Houston | TWA

Nom  Nom PP

VP  V NP (2)

Rule Expansion

Det  that | this | a

LC’s

TopDBotUp

E.g.


Top-Down Parser

  • Builds from the root S node to the leaves

  • Assuming we build all trees in parallel:

    • Find all trees with root S (or all rules w/lhs S)

    • Next expand all constituents in these trees/rules

    • Continue until leaves are pos

    • Candidate trees failing to match pos of input string are rejected (e.g. Book that flight matches only one subtree)


Top-Down Search Space for CFG (expanding only leftmost leaves)

SSS

NPVPAuxNPVPVP

S S S SSS

NP VPNP VP Aux NP VPAux NP VPVP VP

Det NomPropNDet NomPropN V NPV

Det Nom

N


Bottom-Up Parsing

  • Parser begins with words of input and builds up trees, applying grammar rules whose rhs match

    • Book that flight

      NDetNVDetN

      BookthatflightBookthatflight

    • ‘Book’ ambiguous (2 pos appear in grammar)

    • Parse continues until an S root node reached or no further node expansion possible


Two Candidates: One Successful Parse

S

VP

VPNPNP

NomNom

VDetNVDetN

BookthatflightBookthatflight

S ~  VP NP


What’s right/wrong with….

  • Top-Down parsers – they never explore illegal parses (e.g. which can’t form an S) -- but waste time on trees that can never match the input

  • Bottom-Up parsers – they never explore trees inconsistent with input -- but waste time exploring illegal parses (with no S root)

  • For both: find a control strategy -- how explore search space efficiently?

    • Pursuing all parses in parallel or backtrack or …?

    • Which rule to apply next?

    • Which node to expand next?


A Possible Top-Down Parsing Strategy

  • Depth-first search:

    • Agenda of search states: expand search space incrementally, exploring most recently generated state (tree) each time

    • When you reach a state (tree) inconsistent with input, backtrack to most recent unexplored state (tree)

  • Which node to expand?

    • Leftmost or rightmost

  • Which grammar rule to use?

    • Order in the grammar? How?


Top-Down, Depth-First, Left-Right Strategy

  • Initialize agenda with ‘S’ tree and ptr to first word (cur)

  • Loop: Until successful parse or empty agenda

    • Apply next applicable grammar rule to leftmost unexpanded node (n) of current tree (t) on agenda and push resulting tree (t’) onto agenda

      • If n is a POS category and matches the POS of cur, push new tree (t’’) onto agenda and increment cur

      • Else pop t’ from agenda

    • Final agenda contains history of successful parse

  • Does this flight include a meal?


Fig 10.7

CFG


Left Corners: Top-Down Parsing with Bottom-Up Filtering

  • We saw: Top-Down, depth-first, L2R parsing

    • Expands non-terminals along the tree’s left edge down to leftmost leaf of tree

    • Moves on to expand down to next leftmost leaf…

    • Note: In successful parse, current input word will be first word in derivation of node the parser currently processing

    • So….look ahead to left-corner of the tree

      • B is a left-corner of A if A =*=> Bα

      • Build table with left-corners of all non-terminals in grammar and consult before applying rule


Left Corners


Left-Corner Table for CFG


Left Recursion vs. Right Recursion

  • Depth-first search will never terminate if grammar is left recursive (e.g. NP --> NP PP)


  • Solutions:

    • Rewrite the grammar (automatically?) to a weakly equivalent one which is not left-recursive

      e.g. The man {on the hill with the telescope…}

      NP  NP PP (wanted: Nom plus a sequence of PPs)

      NP  Nom PP

      NP  Nom

      Nom  Det N

      …becomes…

      NP  Nom NP’

      Nom  Det N

      NP’  PP NP’ (wanted: a sequence of PPs)

      NP’  e

      • Not so obvious what these rules mean…


  • Harder to detect and eliminate non-immediate left recursion

    • NP --> Nom PP

    • Nom --> NP

  • Fix depth of search explicitly

  • Rule ordering: non-recursive rules first

    • NP --> Det Nom

    • NP --> NP PP


  • An Exercise: The city hall parking lot in town

    • NP NP NP PP

    • NP  Det Nom

    • NP  Adj Nom

    • NP  Nom Nom

    • Nom  NP Nom

    • Nom  N

    • PP  Prep NP

    • N  city | hall | lot | town

    • Adj  parking

    • Prep  to | for | in


    Another Problem: Structural ambiguity

    • Multiple legal structures

      • Attachment (e.g. I saw a man on a hill with a telescope)

      • Coordination (e.g. younger cats and dogs)

      • NP bracketing (e.g. Spanish language teachers)


    NP vs. VP Attachment


    • Solution?

      • Return all possible parses and disambiguate using “other methods”


    Summing Up

    • Parsing is a search problem which may be implemented with many control strategies

      • Top-Down or Bottom-Up approaches each have problems

        • Combining the two solves some but not all issues

      • Left recursion

      • Syntactic ambiguity

    • Next time: Making use of statistical information about syntactic constituents

      • Read Ch 12


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