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LING 438/538 Computational Linguistics. Sandiway Fong Lecture 25: 11/21. Administrivia. Lecture schedule (from last time) Tuesday 21st November Homework #6: Context-free Grammars and Parsing due Tuesday 28th Thursday 23rd November Turkey Day Tuesday 28th November Thursday 30th November

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LING 438/538 Computational Linguistics


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    1. LING 438/538Computational Linguistics Sandiway Fong Lecture 25: 11/21

    2. Administrivia • Lecture schedule (from last time) • Tuesday 21st November • Homework #6: Context-free Grammars and Parsing • due Tuesday 28th • Thursday 23rd November • Turkey Day • Tuesday 28th November • Thursday 30th November • Homework #7: Machine Translation • due December 7th • 538 Presentations • Tuesday 5th December • Homework #7: Machine Translation • 538 Presentations

    3. Administrivia • 538 Presentations: assignments

    4. Last Time • Chapter 10: • Parsing with Context-Free Grammars • Top-down Parsing • Prolog’s DCG rule system • Left recursion • Left-corner idea • Bottom-up Parsing • Dotted rules • LR parsing: shift and reduce operations

    5. LR(0) parsing An example of bottom-up tabular parsing Similar to the top-down Earley algorithm described in the textbook in that both methods use the idea of dotted rules LR is more efficient it computes the dotted rules offline (during parser/grammar construction) Earley computes the dotted rules at parse time LR actions Shift: read an input word i.e. advance current input word pointer to the next word Reduce: complete a nonterminal i.e. complete parsing a grammar rule Accept: complete the parse i.e. start symbol (e.g. S) derives the terminal string Bottom-Up Parsing

    6. Dotted Rule Notation “dot” used to indicate the progress of a parse through a phrase structure rule examples vp --> v . np means we’ve seen v and predict np np --> . d np means we’re predicting a d (followed by np) vp --> vp pp. means we’ve completed a vp state a set of dotted rules encodes the state of the parse kernel vp --> v . np vp --> v . completion (of predict NP) np --> . d n np --> . n np --> . np cp Tabular Parsing

    7. Tabular Parsing • compute possible states by advancing the dot • example: • (Assume d is next in the input) • vp --> v . np • vp --> v . (eliminated) • np --> d . n • np --> . n (eliminated) • np --> . np cp

    8. Dotted rules example State 0: s -> . np vp np -> .d np np -> .n np -> .np pp possible actions shiftd and go to new state shiftn and go to new state Creating new states State 1 NP -> D . N S -> . NP VP NP -> . D N NP -> . N NP -> . NP PP NP -> N . State 0 State 2 Tabular Parsing shift d shift n

    9. State 3 NP -> D N . State 1 NP -> D . N S -> . NP VP NP -> . D N NP -> . N NP -> . NP PP NP -> N . State 0 State 2 Tabular Parsing • State 1: Shift N, goto State 2

    10. State 3 NP -> D N . State 1 NP -> D . N S -> . NP VP NP -> . D N NP -> . N NP -> . NP PP [V hit ] … [N man] [D a ] NP -> N . Input • state 3 Stack State 0 State 2 Tabular Parsing shift n shift d • Shift • take input word, and • place on stack

    11. State 3 NP -> D N . State 1 NP -> D . N S -> . NP VP NP -> . D N NP -> . N NP -> . NP PP NP -> N . State 0 State 2 Tabular Parsing • State 2: Reduce action NP -> N .

    12. [NP milk] Tabular Parsing • Reduce NP -> N . • pop [N milk] off the stack, and • replace with [NP [N milk]] on stack [V is ] … [N milk] Input • State 2 Stack

    13. State 3 NP -> D N . State 1 NP -> D . N S -> . NP VP NP -> . D N NP -> . N NP -> . NP PP NP -> N . State 0 State 2 Tabular Parsing • State 3: Reduce NP -> D N .

    14. [NP[D a ][N man]] Tabular Parsing • Reduce NP -> D N . • pop [N man] and [D a] off the stack • replace with [NP[D a][N man]] [V hit ] … [N man] [D a ] Input • State 3 Stack

    15. State 2 NP -> N . State 4 S -> . NP VP NP -> . D N NP -> . N NP -> . NP PP S -> NP . VP NP -> NP . PP VP -> . V NP VP -> . V VP -> . VP PP PP -> . P NP State 0 Tabular Parsing • State 0: Transition NP

    16. Tabular Parsing • for both states 2 and 3 • NP -> N . (reduce NP -> N) • NP -> D N . (reduce NP -> D N) • after Reduce NP operation • Goto state 4 • notes: • states are unique • grammar is finite • procedure generating states must terminate since the number of possible dotted rules

    17. Tabular Parsing

    18. Tabular Parsing • Observations • table is sparse • example • State 0, Input: [V ..] • parse fails immediately • in a given state, input may be irrelevant • example • State 2 (there is no shift operation) • there may be action conflicts • example • State 1: shift D, shift N • more interesting cases • shift-reduce and reduce-reduce conflicts

    19. Tabular Parsing • finishing up • an extra initial rule is usually added to the grammar • SS --> S . $ • SS = start symbol • $ = end of sentence marker • input: • milk is good for you $ • accept action • discard $ from input • return element at the top of stack as the parse tree

    20. LR Parsing in Prolog • Recap • finite state machine • each state represents a set of dotted rules • example • S --> . NP VP • NP --> . D N • NP --> . N • NP --> . NP PP • we transition, i.e. move, from state to state by advancing the “dot” over terminal and nonterminal symbols

    21. LR Parsing in Prolog • Plan: • formally describe a LR finite state machine construction process • define the parse procedure • parse(Sentence,Tree) in terms of the LR finite state machine • run • John saw the man with a telescope • ? - parse([john,saw,the,man,with,a,telescope],T). which produces two parses (PP-attachment ambiguity)

    22. Grammar • assume grammar rules and lexicon: • rule(s,[np,vp]).convenient format for the LR(0) generator • rule(np,[d,n]). • rule(np,[n]). • rule(np,[np,pp]). • rule(vp,[v,np]). • rule(vp,[v]). • rule(vp,[vp,pp]). • rule(pp,[p,np]). • lexicon(the,d). lexicon(a,d). • lexicon(man,n). lexicon(john,n). lexicon(telescope,n). • lexicon(saw,v). lexicon(v,runs). • lexicon(with,p).

    23. Grammar • extra definitions • :- dynamic rule/2. • start(ss). • rule(ss,[s,$]). • nonT(ss). nonT(s). nonT(np). nonT(vp). nonT(pp). • term(n). term(v). term(p). term(d). term($). • notes: • $ = end of sentence marker • Prolog programming trick • declaring rule/2 as dynamic allows us to use the builtin clause(rule(LHS,RHS),true,Ref) to keep a pointer (Ref) to a particular rule

    24. Grammar Rule Predicates • define • %%% Assume grammar rules are stored as database facts • %%% rule(LHS,RHS) • ruleLHS(NonT,Ref) :- clause(rule(NonT,_),true,Ref). • ruleRHS(RHS,Ref) :- clause(rule(_,RHS),true,Ref). • ruleElements(LHS,RHS,Ref) :- % assume Ref instantiated • clause(rule(LHS,RHS),true,Ref). • note • Ref (when instantiated) is a pointer to an instance of rule(LHS,RHS).

    25. A Counter in Prolog • define • stateCounter(N) to hold the current state number (N = 0,1,2,3…) • define predicates • resetStateCounter :- • retractall(stateCounter(_)), • assert(stateCounter(0)). • incStateCounter :- • retract(stateCounter(X)), • Y is X + 1, • assert(stateCounter(Y)). Prolog builtins used: retract/1 - removes matching item from the database retractall/1 - removes all matching items from the database assert/1 - adds item to the database

    26. Data Structures • define cfsm/3 • cfsm(L,CFSet,N) “state configuration” • CFSet = list of dotted rules for state N • L = |CFSet| (used for quicker lookup) • define cf/3 • cf(Ref,I) “dotted rule configuration” • Ref points to a rule(LHS,RHS) • (I = 0,1,2…) is the index of the “dot” in RHS

    27. SS --> . S $ S --> . NP VP NP --> . D N NP --> . N NP --> . NP PP State 0 Build FSA • initially • R1 = rule(ss,[s,$]). • ss --> . s $ • cf(R1,0) • do a closure on the dotted rule, adding • s --> . np vp • np --> . d n • …

    28. Build FSM: Closure Operation • define • mkStartCF(cf(Ref,0)) :- start(Start),ruleLHS(Start,Ref). • call • mkStartCF(StartCF), • closure([StartCF],S0), • define closure/2 recursively • closure(CFSet,CFSet1) :- • dotNonT(CFSet,NonT), • predict(NonT,CFSet,CFSet2), • closure(CFSet2,CFSet1). • closure(CFSet,CFSet).

    29. Build FSM: Closure Operation • define dotNonT/2 to pick out possible instances ofYinX --> … .Y … • dotNonT([cf(Ref,Pos)|_],NonT) :- • dotNonT1(Ref,Pos,NonT). • dotNonT([_|L],NonT) :- dotNonT(L,NonT). • dotNonT1(Ref,Pos,NonT) :- • ruleRHS(RHS,Ref), nth(Pos,RHS,NonT), nonT(NonT). • notes • dotNonT/2 works just like list member/2 • nth(N,L,X) picks out (N+1)th element (X) in list L

    30. Build FSM: Closure Operation • define predict/3 to add new dotted rules for NonT • predict(NonT,CFSet,NewCFSet) :- • findall(cf(Ref,0),ruleLHS(NonT,Ref),NewCFs), • merge(NewCFs,CFSet,NewCFSet,[],new). • define merge/3 to add new dotted rules only if there’re not already present in CFSet • merge([],L,L,Flag,Flag). • merge([cf(Ref,Pos)|L],CFSet,CFSet1,Flag,Flag1) :- % already present • member(cf(Ref,Pos),CFSet), • merge(L,CFSet,CFSet1,Flag,Flag1). • merge([CF|L],CFSet,CFSet1,_,Flag) :- % CF is new • merge(L,[CF|CFSet],CFSet1,new,Flag). • note • the variable Flag ([]/new) is used to make sure something has been added to CFSet

    31. Build FSM: Closure Operation • call • mkStartCF(StartCF), • closure1([StartCF],S0), • resetStateCounter, • length(S0,L), • cfsmEntry(S0,L), • define storage predicate cfsmEntry/2 • cfsmEntry(CFSet,L) :- • stateCounter(State), • incStateCounter, • asserta(cfsm(L,CFSet,State)). • cfsm(L,CFSet,N) “state configuration” • CFSet = list of dotted rules for state N • L = |CFSet| (used for quicker lookup)

    32. Build FSM: Build new state • define buildState/1 • buildState(CFSet,S1) :- • transition(CFSet,Symbol,CFSet1), • length(CFSet1,L), • addCFSet(CFSet1,L,S2), • assert(goto(S1,Symbol,S2)), • fail. • buildState(_,_). • notes • transition/3 produces a new CFSet by advancing the dot over Symbol • addCFSet/3 will add a new state represented by CFSet1 (if it doesn’t already exist) • State transitions represented by goto(S1,Symbol,S2)

    33. State 4 S --> . NP VP NP --> . D N NP --> . N NP --> . NP PP S --> NP . VP NP --> NP . PP VP --> . V NP VP --> . V VP --> . VP PP PP --> . P NP State 0 Build FSM: Build new state • define transition/3 • transition(CFSet,Symbol,CFSet1) :- • pickSymbol(CFSet,Symbol), • advanceDot(CFSet,Symbol,CFSet2), • closure(CFSet2,CFSet1). • Note: pickSymbol/2 picks a symbol next to a dot in a dotted rule in CFSet • define advanceDot/3 • advanceDot([cf(Ref,Pos)|L],Symbol,[cf(Ref,Pos1)|CFSet]) :- • ruleRHS(RHS,Ref), nth(Pos,RHS,Symbol), • !, • Pos1 is Pos+1, • advanceDot(L,Symbol,CFSet). • advanceDot([_|L],Symbol,CFSet) :- !, advanceDot(L,Symbol,CFSet). • advanceDot([],_,[]).

    34. Build FSM: Build new state • define addCFSet/3 • addCFSet(CFSet,L,S) :- % CFSet already established • findCFSet(CFSet,S,L), • !. • addCFSet(CFSet,L,S) :- % CFSet is new state #N • cfsmEntry(CFSet,L,S). % add it • Note: • findCFSet/3 will succeed only if CFSet exists in the current cfsm/3 database • cfsmEntry/3 defined earlier will increment the state number (S) and perform: • ?- asserta(cfsm(L,CFSet,S)).

    35. Build Actions • two main actions • Shift • move a word from the input onto the stack • Example: • NP --> .D N • Reduce • build a new constituent • Example: • NP --> D N.

    36. Build Actions • Machine components [V hit ] … Input [N man] [D a ] 3 2 0 • A machine operation step (action) will have signature: • CS x Input x SS  CS’ x Input’ x SS’ • where • CS = control stack • SS = (constituent) structure stack Structure Stack (items) Control Stack (states)

    37. Build Actions: shift action • example • shift(n) • code • action(S, CS, Input, SS, CS2, Input2, SS2 ) :- • Input = [Item|Input2], • category(Item,n), • goto(S,n,S2), • CS2 = [S2|CS], • SS2 = [Item|SS]. • notes: (changes) • Input2 is Input minus Item • SS2 is SS plus Item • CS2 is CS plus S2 from goto(S,n,S2)

    38. Build Actions: shift action • calling pattern for action/7 • given values for: • current state (S) • control and structure stacks (CS,SS) • compute new values of: • state (S2) • control and structure stacks (CS2,SS2) action(S, CS, Input, SS, CS2, Input2, SS2 ) Given Compute

    39. Build Actions: reduce action • example • reduce NP --> D N. • code • action(S, CS, Input, SS, CS2, Input2, SS2 ) :- • Input = Input2, • SS = [N,D|SS3], • SS2 = [np(D,N)|SS3], • CS = [_,_,S1|CS3], • CS2 = [S2,S1|CS3], • goto(S1,np,S2). • notes • input is unchanged • pop 2 items off the stacks • goto is not based on current state

    40. Build Actions • define shift/reduce action generation procedure • buildActions :- • cfsm(_,CFSet,State), • actions(CFSet,Instructions), • genActions(State,Instructions), • fail. • buildActions. • define actions/2 • actions([],[]). • actions([CF|CFs],L) :- • reduceAction(CF,L1), • shiftAction(CF,L2), • append(L1,L2,L3), • actions(CFs,L4), • union(L3,L4,L) % should be no duplicate actions

    41. Build Actions • define shift and reduce actions • reduceAction(cf(Ref,Pos),[reduce(Ref)]) :- • ruleRHS(RHS,Ref), • length(RHS,Pos), % finds config. A-->. • !. • reduceAction(_,[]). • % assume that Symbol in Vt • shiftAction(cf(Ref,Pos),[shift(Symbol)]) :- • ruleRHS(RHS,Ref), % finds config. A-->.a • nth(Pos,RHS,Symbol), • term(Symbol), • !. • shiftAction(_,[]). • builds sequences of instructions of the form • [shift(n), reduce(R3)]etc.

    42. Build Actions • define procedure genActions/2 • which turns instructions such as: • shift(n) • into code like • action(S, CS, Input, SS, CS2, Input2, SS2 ) :- • Input = [Item|Input2], • category(Item,n), • goto(S,n,S2), • CS2 = [S2|CS2].

    43. Build Actions • genActions/2 • processes a list of actions for a given state S • genActions(_,[]). • genActions(S,[Action|As]) :- • nl, • actionClause(S,Action,Clause), • write(Clause), write('.'), • genActions(S,As). Prolog builtins nl - writes a newline to standard output write/1 - writes supplied argument to standard output

    44. Build Actions: shift • generate action/7 for shift • % shifting a $ • actionClause(State,shift($),action(State,_,[$],SS,accept,[],SS)) :- !. • % shifting anything other than a $ • actionClause(State,shift(Symbol), • (action(State,CS,[I|Is],SS,[S|CS],Is,[I|SS]) :- • functor(I,Symbol,_), • goto(State,Symbol,S))). • note: • see words/2 later • assume input item is of form c(word), e.g. n(john)

    45. Build Actions: reduce • generate action/7 for reduce • actionClause(State,reduce(Ref), • (action(State,CS,I,SS,[S2,Last|CS1],I,[Item|SS1]) :- • goto(Last,NT,S2))) :- • ruleElements(NT,RHS,Ref), • popStk(RHS,CS,Last,CS1), • popAndLink(RHS,SS,SS1,L), • Item =.. [NT|L]. • note • popStk/4 and popAndLink/4 both generate code to pop the control and structure stacks

    46. example of LR Machine constructed % State 8: pp->.p np vp->vp .pp s->np vp. goto(4,vp,8). % State 9: vp->vp pp. goto(8,pp,9). goto(8,p,6). goto(7,d,2). goto(7,n,3). % State 10: pp->.p np np->np .pp vp->v np. goto(7,np,10). goto(10,pp,5). goto(10,p,6). goto(6,d,2). goto(6,n,3). % State 11: pp->.p np np->np .pp pp->p np. goto(6,np,11). goto(11,pp,5). goto(11,p,6). % State 12: np->d n. goto(2,n,12). % State 13: ss->s $. goto(1,$,13). LR Machine: goto table

    47. LR Machine: action table • example of action table constructed • action(State,CS,Input,SS,CS’,Input’,SS’) • % 7 • action(7,_14,[_20|_18],_16,[_22|_14],_18,[_20|_16]):-functor(_20,n,_32),goto(7,n,_22). • action(7,_58,[_64|_62],_60,[_66|_58],_62,[_64|_60]):-functor(_64,d,_76),goto(7,d,_66). • action(7,[_38,_10|_11],_03,[_44|_13],[_08,_10|_11],_03,[vp(_44)|_13]):-goto(_10,vp,_08). • % 6 • action(6,_78,[_84|_82],_80,[_86|_78],_82,[_84|_80]):-functor(_84,n,_96),goto(6,n,_86). • action(6,_22,[_28|_26],_24,[_30|_22],_26,[_28|_24]):-functor(_28,d,_40),goto(6,d,_30). • % 5 • action(5,[_68,_70,_38|_39],_31,[_78,_82|_41],[_36,_38|_39],_31,[np(_82,_78)|_41]):-goto(_38,np,_36).

    48. Parser • define parse/2 as follows • parse(Words,Parse) :- • words(Words,L), • machine([0],L,[],Parse). • machine(CS,Input,SS,Parse) :- • CS = accept • -> SS = [Parse] • ; CS = [State|_], • action(State,CS,Input,SS,CS2,Input2,SS2), • machine(CS2,Input2,SS2,Parse). • words([],[$]). • words([W|Ws],[I|Is]) :- lexicon(W,C), I =.. [C,W], words(Ws,Is).

    49. Administrivia • Prolog code available on the course webpage • files • grammar0.pl - example grammar • lr0.pl - LR(0) parser/generator • machine0.pl - generated tables

    50. How to use steps ?- [grammar0]. (consult toy grammar) ?- [lr0]. (consult LR code) ?- build. (constructs goto table) ?- buildActions. (constructs shift/reduce actions) How to use (saving output to a file) steps ?- [grammar0]. (consult toy grammar) ?- [lr0]. (consult LR code) ?- tell(‘filename.pl’). (redirect screen output to filename.pl) ?- build. (constructs goto table) ?- buildActions. (constructs shift/reduce actions) ?- told. (close filename.pl) LR Parsing in Prolog