LING 388: Language and Computers

Sandiway Fong

Lecture 11: 10/4

Administrivia

• Homework #2– has been graded– you should get an email in a day or so

• Reservation (tentative)– Lab class– practice and homework #3 on context-free grammar parsing– next Monday (11th October)– meet in SBS 224, Instructional Computing Lab (not here)

Last Time

• Context-Free Grammars (CFG)– from acceptor to parser– add an extra argument to grammar rules

• x --> y, z.• x(x(Y,Z)) --> y(Y), z(Z).

– extra argument changes the expressive power of the rules

• regular grammar rules + extra argument can handle the non-regular language anbn

Today’s Topic

• Context-free grammar technology + bells and whistles are at the core of parsing sentences

– we’re going to keep exploring for the next few lectures how to implement natural language fragments

– today: more on extra arguments ...

Extra Argument and Phrase Structure

• Grammar from Lecture #10:– s(s(Y,Z)) --> np(Y), vp(Z).– np(np(Y)) --> pronoun(Y).– np(np(det(the),n(ball))) --> [the,ball].– pronoun(i) --> [i].– pronoun(we) --> [we].– vp(vp(Y)) --> unergative(Y). – vp(vp(Y,Z)) --> transitive(Y), np(Z).– unergative(v(ran)) --> [ran].– transitive(v(hit)) --> [hit].

• Query:– ?- s(X,[john,hit,the,ball],[]).

Result: parse tree

Extra Argument and Phrase Structure

• Examples:s

np vp

v np

det n

the ball

hit

i

s

np vp

v

ran

we

?- s(X,[we,ran],[]).

X = s(np(we),vp(v(ran)))?- s(X,[i,hit,the,ball],[]).X = s(np(i),vp(v(hit),np(det(the),n(ball))))

Extra Argument and Determiner-Noun Agreement

• Idea:– We can also use the extra argument to impose constraints

between constituents within a DCG rule

• Example: – English determiner-noun number agreement– Data:

• the man• the men• a man• *a men

– Lexical Features:• man singular• men plural

Extra Argument and Determiner-Noun Agreement

• Data:– the man/men– a man/*a men

• Grammar:– s(s(Y,Z)) --> np(Y), vp(Z).– np(np(Y)) --> pronoun(Y).– np(np(det(the),n(ball))) --> [the,ball].– pronoun(i) --> [i].– pronoun(we) --> [we].– vp(vp(Y)) --> unergative(Y). – vp(vp(Y,Z)) --> transitive(Y), np(Z).– unergative(v(ran)) --> [ran].– transitive(v(hit)) --> [hit].

np --> det, common_noun.det --> [the].det --> [a].common_noun--> [ball].common_noun--> [man].common_noun --> [men].

np --> det, common_noun.det --> [the].det --> [a].common_noun--> [ball].common_noun--> [man].common_noun --> [men].

Extra Argument and Determiner-Noun Agreement

• Data:– the man/men– a man/*a men

• Grammar:– s(s(Y,Z)) --> np(Y), vp(Z).– np(np(Y)) --> pronoun(Y).– np(np(det(the),n(ball))) --> [the,ball].– pronoun(i) --> [i].– pronoun(we) --> [we].– vp(vp(Y)) --> unergative(Y). – vp(vp(Y,Z)) --> transitive(Y), np(Z).– unergative(v(ran)) --> [ran].– transitive(v(hit)) --> [hit].

np --> det, common_noun.det --> [the].det --> [a].common_noun--> [ball].common_noun--> [man].common_noun --> [men].

np(np(D,N)) --> det(D), common_noun(N).det(det(the)) --> [the].det(det(a)) --> [a].common_noun(n(ball)) --> [ball].common_noun(n(man)) --> [man].common_noun(n(men)) --> [men].

np(np(D,N)) --> det(D), common_noun(N).det(det(the)) --> [the].det(det(a)) --> [a].common_noun(n(ball)) --> [ball].common_noun(n(man)) --> [man].common_noun(n(men)) --> [men].

Extra Argument and Determiner-Noun Agreement

• Data:– the man/men– a man/*a men

• Grammar:– s(s(Y,Z)) --> np(Y), vp(Z).– np(np(Y)) --> pronoun(Y).– np(np(D,N)) --> det(D), common_noun(N).– det(det(the)) --> [the].– det(det(a)) --> [a].– common_noun(n(ball)) --> [ball].– common_noun(n(man)) --> [man].– common_noun(n(men)) --> [men].– pronoun(i) --> [i].– pronoun(we) --> [we].– vp(vp(Y)) --> unergative(Y). – vp(vp(Y,Z)) --> transitive(Y), np(Z).– unergative(v(ran)) --> [ran].– transitive(v(hit)) --> [hit].

• Lexical Features•man singular•men plural

•Rules•the can combine with singular or plural nouns•a can combine only with singular nouns

Extra Argument and Determiner-Noun Agreement

• Data:– the man/men– a man/*a men

• Grammar: (NP section)– np(np(Y)) --> pronoun(Y).– np(np(D,N)) --> det(D), common_noun(N,Number).– det(det(the)) --> [the].– det(det(a)) --> [a].– common_noun(n(ball),sg) --> [ball].– common_noun(n(man),pl) --> [man].– common_noun(n(men),pl) --> [men].– pronoun(i) --> [i].– pronoun(we) --> [we].

•Idea:specify singular (sg) and plural (pl) for common nouns using an extra argument

•Rules•the can combine with singular or plural nouns•a can combine only with singular nouns

Extra Argument and Determiner-Noun Agreement

• Data:– the man/men– a man/*a men

• Grammar: (NP section)– np(np(Y)) --> pronoun(Y).– np(np(D,N)) --> det(D,Number),

common_noun(N,Number).– det(det(the),sg) --> [the].– det(det(the),pl) --> [the].– det(det(a),sg) --> [a].– common_noun(n(ball),sg) --> [ball].– common_noun(n(man),pl) --> [man].– common_noun(n(men),pl) --> [men].– pronoun(i) --> [i].– pronoun(we) --> [we].

•Idea:give determiners a number feature as welland make it agree with the noun

•Rules•the can combine with singular or plural nouns•a can combine only with singular nouns

Extra Argument and Determiner-Noun Agreement

• Query:– ?- np(X,[the,men],[]).– Note: we need not start with non-terminal symbol s,

i.e. parse a full sentence– Prolog DCG rules can be independently accessed

• Computation tree: – ?- np(X,[the,men],[]). X = np(D,N)

• ?- det(D,Number,[the,men],L).• ?- common_noun(N,Number,L,[]).

– ?- det(D,Number,[the,men],L). Rule #3• D = det(the) Number = sg L = [men]

– ?- common_noun(N,sg,[men],[]). Rule #8• No

– Retry (rule #3 led to failure)– ?- det(D,Number,[the,men],L). Rule #4

• D = det(the) Number = pl L = [men]– ?- common_noun(N,pl,[men],[]). Rule #8

• Yes N = n(men)

• X = np(det(the),n(men))

1. np(np(Y)) --> pronoun(Y).

2. np(np(D,N)) --> det(D,Number), common_noun(N,Number).

3. det(det(the),sg) --> [the].4. det(det(the),pl) --> [the].5. det(det(a),sg) --> [a].6. common_noun(n(ball),sg) -->

[ball].7. common_noun(n(man),pl) -->

[man].8. common_noun(n(men),pl) -->

[men].9. pronoun(i) --> [i].

10. pronoun(we) --> [we].

Extra Argument and Determiner-Noun Agreement

• Data:– the man/men– a man/*a men

• Query:– ?- np(X,[a,men],[]).

• Computation tree: – ?- np(X,[a,men],[]). X = np(D,N)

• ?- det(D,Number,[a,men],L).• ?- common_noun(N,Number,L,[]).

– ?- det(D,Number,[a,men],L). Rule #5• D = det(a) Number = sg L = [men]

– ?- common_noun(N,sg,[men],[]). Rule #8• No

1. np(np(Y)) --> pronoun(Y).

2. np(np(D,N)) --> det(D,Number), common_noun(N,Number).

3. det(det(the),sg) --> [the].4. det(det(the),pl) --> [the].5. det(det(a),sg) --> [a].6. common_noun(n(ball),sg) -->

[ball].7. common_noun(n(man),pl) -->

[man].8. common_noun(n(men),pl) -->

[men].9. pronoun(i) --> [i].

10. pronoun(we) --> [we].

Extra Argument and Determiner-Noun Agreement

• Simplifying the grammar:– det(det(the),sg) --> [the].– det(det(the),pl) --> [the].– det(det(a),sg) --> [a].

• Grammar is ambiguous:– two rules for determiner the– can see the effect in the computation tree

• retry needed to get “the men” to parse• Agreement Rule (revisited):

• the can combine with singular or plural nouns• i.e. the doesn’t care about the number of the noun

• DCG Rule:• np(np(D,N)) --> det(D,Number), common_noun(N,Number).

– det(det(the),_) --> [the].Note: _ is a variableused underscore character because I don’t care about the name of the variable

Extra Argument and Determiner-Noun Agreement

• Revisit Query:– ?- np(X,[the,men],[]).

• Computation tree: – ?- np(X,[the,men],[]). X = np(D,N)

• ?- det(D,Number,[the,men],L).• ?- common_noun(N,Number,L,[]).

– ?- det(D,Number,[the,men],L). Rule #3• D = det(the) Number = _ L = [men]

– ?- common_noun(N,_,[men],[]). Rule #7• Yes N = n(men) _ = pl

• X = np(det(the),n(men))• Advantage:

– no need for retry (ambiguity removed)

1. np(np(Y)) --> pronoun(Y).

2. np(np(D,N)) --> det(D,Number), common_noun(N,Number).

3. det(det(the),_) --> [the].4. det(det(a),sg) --> [a].5. common_noun(n(ball),sg) -->

[ball].6. common_noun(n(man),pl) -->

[man].7. common_noun(n(men),pl) -->

[men].8. pronoun(i) --> [i].

9. pronoun(we) --> [we].