1. CSA4050: Advanced Topics in NLP
Semantics IV
Partial Execution
Proper Noun
Transitive Verb Phrase

2. Partial Execution
Partial execution involves the replacing of certain runtime computations with changes to the source of the Prolog program itself.
For example, we can replace the rule: s(S) --> np(NP), vp(VP) { reduce(NP,VP,S) }. with s(S) --> np(VP^S), vp(S).
This is because the computation of reduce involves only the mutual binding of several variables.
October 2004
CSA4050 Advanced NLP

3. How it works 1. match reduce(A^F,A,F) 2. rewrite 3. rename
s(S) --> np(NP), vp(VP) { reduce(NP,VP,S)}.
1. match reduce(A^F,A,F)
2. rewrite
s(F) --> np(A^F), vp(A).
3. rename
s(S) --> np(VP^S), vp(VP).
October 2004
CSA4050 Advanced NLP

4. Exercise
What is the result of eliminating the reduce clause by partial execution in the following rule?
np(NP) --> d(D), n(N), {reduce(D,N,NP)}.
October 2004
CSA4050 Advanced NLP

5. Answer 1. match reduce(A^F,A,F) 2. rewrite 3. rename
np(NP) --> d(D), n(N) { reduce(D,N,NP)}.
1. match reduce(A^F,A,F)
2. rewrite
np(F) --> d(A^F), n(A).
3. rename
np(NP) --> d(N^NP), n(N).
October 2004
CSA4050 Advanced NLP

6. DCG with Quantification Program 4
% grammar
s(S) --> np(VP^S), vp(VP).
np(NP) --> d(N^NP), n(N).
vp(VP) --> v(VP).
% lexicon
v(X^walk(X)) > [walks].
n(X^man(X)) > [man].
n(suzie) --> [‘Suzie’].
det(RL^SL^all(X,R,S) > [every], {reduce(RL,X,R), reduce(SL,X,S) }.
October 2004
CSA4050 Advanced NLP

7. Handling Proper Nouns ?- s(X,['Suzie',walks],[ ]).
The grammar handles every man walks X = all(_G, man(_G), walk(_G))
Will this grammar parse Suzie walks?
Let’s try it!
?- s(X,['Suzie',walks],[ ]).
October 2004
CSA4050 Advanced NLP

8. ?- s(X,['Suzie',walks],[ ]).
Call: (8) s(_G492, ['Suzie', walks], []) ?
Call: (9) np(_L183, ['Suzie', walks], _L184) ?
Call: (10) pn(_L183, ['Suzie', walks], _L184) ?
Exit: (10) pn(suzie, ['Suzie', walks], [walks]) ?
Exit: (9) np(suzie, ['Suzie', walks], [walks]) ?
Call: (9) vp(_L185, [walks], _L186) ?
Call: (10) iv(_L185, [walks], _L186) ?
Exit: (10) iv(_G556^walk(_G556), [walks], []) ?
Exit: (9) vp(_G556^walk(_G556), [walks], []) ?
Call: (9) reduce(suzie, _G556^walk(_G556), _G492) ?
Fail: (9) reduce(suzie, _G556^walk(_G556), _G492)?
suzie is not a function
October 2004

9. Handling Proper Nouns Problem is with the “type” of LF of Suzie.
We require that LF of Suzie has the same type as any other NP - such as every man, i.e.
As a lambda expression it would be λp.p(suzie).
In Prolog we can regard this as a function from [VP] to [S] such that reduce(VP,john,S) holds.
October 2004
CSA4050 Advanced NLP

10. DCG with Quantification Program 4
% grammar
s(S) --> np(VP^S), vp(VP).
np(NP) --> n(NP).
np(NP) --> d(N^NP), n(N).
vp(VP) --> v(VP).
% lexicon
v(X^walk(X)) > [walks].
n(X^man(X)) > [man].
n(VP^S) > [‘Suzie’],
{reduce(VP,suzie,S)}.
det(RL^SL^all(X,R => S) --> [every], {reduce(RL,X,R), reduce(SL,X,S) }.
October 2004
CSA4050 Advanced NLP

11. Exercise 2 Using partial execution, eliminate the reduce clause in
pn(VP^S) --> [‘Suzie’],{reduce(VP,suzie,S)}.
October 2004
CSA4050 Advanced NLP

12. s(X, ['Suzie', walks], [ ]) ?
Call: (7) s(_G292, ['Suzie', walks], []) ? ↓
Exit: (9) pn((suzie^_G357)^_G357, ['Suzie', walks], [walks]) ?
Exit: (9) iv(_G362^walk(_G362), [walks], []) ?
Exit: (8) vp(_G362^walk(_G362), [walks], []) ? :
Call: (8) reduce((suzie^_G357)^_G357, _G362^walk(_G362), _G292) ?
Exit: (8) reduce((suzie^walk(suzie))^walk(suzie), suzie^walk(suzie), walk(suzie)) ?
Exit: (7) s(walk(suzie), ['Suzie', walks], []) ? creep
X = walk(suzie)
October 2004
CSA4050 Advanced NLP

13. Transitive Verb Phases
Transitive verb phrases take an object, e.g. chased a cat
To handle transitive VPs we need another VP rule vp(VP) --> v(V), np(NP).
In this case we have:
V = λx. λy. chased(x,y)
NP = λs.some(w,cat(w),s(w))
Issues:
What is the LF of the resulting VP and
How do the component LFs combine?
October 2004
CSA4050 Advanced NLP

14. λz.some(y,cat(y),chased(z,y))
Resulting VP
λz.some(y,cat(y),chased(z,y))
Note that this has the form of a standard VP that is waiting for a subject, so is compatible with the rest of the grammar.
October 2004
CSA4050 Advanced NLP

15. λz.some(y,cat(y),chased(z,y))
Making VP VP
λz.some(y,cat(y),chased(z,y)) V
λx. λy. chased(x,y)
chased NP
λs.some(w,cat(w),s(w))
some cat
October 2004
CSA4050 Advanced NLP

16. Apply NP to V doesn't work!
λs.some(w,cat(w), s(w)) (λx. λy. chased(x,y)) β
some(w,cat(w), (λy. λx. chased(x,y))(w))
some(w,cat(w), λx.chased(x,w)) NP V
October 2004
CSA4050 Advanced NLP

17. Solution λs.some(w,cat(w), s(w)) ← NP arg λx. λy. chased(x,y)) ← V arg
Need a more complex way of combining V and NP: λNP.λV.λz.NP(V(z))
λs.some(w,cat(w), s(w)) ← NP arg
λx. λy. chased(x,y)) ← V arg
October 2004
CSA4050 Advanced NLP

18. How it works λNP.λV.λz.NP(V(z)) λs.some(w,cat(w), s(w))
λx. λy. chased(x,y))
λ z.λs.some(w,cat(w), s(w)) λx.λy.chased(x,y)(z) β
λ z.λs.some(w,cat(w), s(w)) (λy. chased(z,y))
λ z. some(cat(w), (λy.chased(z,y))(w))
λ z. some(cat(w), chased(z,w))
October 2004
CSA4050 Advanced NLP

19. VP Rule Revisited vp(VP) --> v(V), np(NP), {instructions}.
The instructions encode the combination λNP.λV.λz.NP(V(z)) vp(Z^P) --> v(V2), np(NP),
{reduce(V2,Z,V1),
reduce(NP,V1,P)}.
October 2004
CSA4050 Advanced NLP

20. Program 5 % grammar s(S) --> np(NP), vp(VP), {reduce(NP,VP,S)}.
np(NP) --> n(NP).
np(NP) --> d(D), n(N), {reduce(D,N,NP) }.
vp(VP) --> v(VP).
vp(Z^P)--> v(V2), np(NP),
{reduce(V2,Z,V1), reduce(NP,V1,P)}.
% lexicon
v(X^walk(X)) > [walks].
v(X^Y^chased(X,Y)) --> [chased].
n(X^cat(X)) > [cat].
n(VP^S) > [suzie], {reduce(VP,suzie,S)}.
d(RL^SL^some(X,R,S)) --> [a],
{reduce(RL,X,R),reduce(SL,X,S) }.
October 2004
CSA4050 Advanced NLP

21. Test ?- s(X,[suzie,chased,a,cat],[]). X = some(_G245, cat(_G245),
chased(suzie, _G245))
?- s(X,[a,cat,chased,a,cat],[]).
some(_G266,
cat(_G266),
chased(_G245, _G266))) ;
October 2004
CSA4050 Advanced NLP