1. Packed Computation of Exact Meaning Representations
Iddo Lev
Department of Computer Science
Stanford University

2. Iddo Lev, Packed Computation of Exact Meaning Representations
Outline
 Motivation
 Motivation
 From Syntax to Semantics
 Packed Computation
 Conclusion
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

3. Natural Language Understanding
How can we improve accuracy?
Let’s take it for a moment to the extreme
Exact NLU applications
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

4. Example: Logic Puzzles
Six sculptures—C, D, E, F, G, and H—are to be exhibited in rooms 1, 2, and 3 of an art gallery.
Sculptures C and E may not be exhibited in the same room.
Sculptures D and G must be exhibited in the same room.
If sculptures E and F are exhibited in the same room, no other sculpture may be exhibited in that room.
At least one sculpture must be exhibited in each room, and no more than three sculptures may be exhibited in any room.
1. If sculpture D is exhibited in room 3 and sculptures E and F are exhibited in room 1, which of the following may be true?
(A) Sculpture C is exhibited in room 1.
(B) No more than 2 sculptures are exhibited in room 3.
(C) Sculptures F and H are exhibited in the same room.
(D) Three sculptures are exhibited in room 2.
(E) Sculpture G is exhibited in room 2.
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

5. Example: Logic Puzzles
If sculptures E and F are exhibited in the same room, no other sculpture may be exhibited in that room.
x.[(room(x)  exhibited-in(E,x)  exhibited-in(F,x))  ¬y.sculpture(y)  y  E  y  F  exhibited-in(y,x)]
exact meaning representation:
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

6. Iddo Lev, Packed Computation of Exact Meaning Representations
Example:
MSCS Degree Requirements
A candidate is required to complete a program of 45 units. At least 36 of these must be graded units, passed with an average 3.0 (B) grade point average (GPA) or higher. The 45 units may include no more than 21 units of courses from those listed below in Requirements 1 and 2. …
Has Patrick Davis completed the program?
Can/must Patrick Davis take CS287?
Similar to logic puzzles:
General constraints + specific situation
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

7. Iddo Lev, Packed Computation of Exact Meaning Representations
Exact NLU
More examples
Word problems
Logic puzzles
Math, physics, chemistry questions
Simple regulation texts, controlled language
NL interfaces to databases
Like SQL, but looks like NL
In these tasks
“Almost correct” (“only slightly wrong”) is not good enough
Simple approximations won’t do
E.g. syntactic matching between text and questions
Because answer does not appear explicitly in the text
Need exact calculation of NL meaning representations
Answer needs to be inferred from the text
Need to carefully combine information/meaning throughout the text
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

8. Iddo Lev, Packed Computation of Exact Meaning Representations
Structural Semantics
Need to rely on high-quality meaning representations and linguistic knowledge
In particular, structural semantics
Meaning of functional words
Logical structure of sentences
Essential for exact NLU tasks
Could also improve precision of other NLP tasks
T: Michael Melvill guided a tiny rocket-ship more than 100 kilometers above the Earth.
H: A rocket-ship was guided more than 80 kilometers above the Earth. Follows
H: A rocket-ship was guided more than 120 kilometers above the Earth. Does not follow
Relatively small size of knowledge
Functional: #functional words  400 #grammar rules  400
Lexical: #verb frames  45,000 #nouns > 100,000
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

9. Iddo Lev, Packed Computation of Exact Meaning Representations
My Dissertation
How to map syntactic analysis to meaning representations
How to compute all meaning representations efficiently
Linguistic analysis of advanced NL constructions using the above framework
anaphora (interaction with truth conditions)
comparatives
reciprocals (each other, one another)
same/different
How to translate meaning representations to inference representations (FOL)
Focus of this talk
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

10. Structural Semantics Challenges
When analyzing one sentence:
(1) Bills 2 and 6 are paid on the same day as each other.
it might seem enough to use:
x.day(x)paid-on(bill2,x)paid-on(bill6,x)
But this is not enough when we consider other sentences:
(2) John, Mary, and Frank like each other.
each_other({john,mary,frank}, xy.like(x,y))
Goal
Uniformity: one analysis of “each other” for both (1) and (2).
Should interact correctly with “the same” in (1).
Solution should also be consistent with “different”, “similar”:
Men and women have a different sense of humor (than each other).
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

11. Iddo Lev, Packed Computation of Exact Meaning Representations
Outline 
 Motivation
 From Syntax to Semantics
 Packed Computation
 Conclusion
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

12. From Syntax to Semantics
How do we get from one parse tree to a semantic representation?
Classic Method (Montague): one-to-one correspondence: assign a lambda-term to each syntactic node
S x. [dog(x)  bark(x)]
λR. x. [dog(x)  R(x)] NP VP
| V barks
λz. bark(z)
Det every
λP.λR. x. [P(x)  R(x)]
Noun dog
λy.dog(y)
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Iddo Lev, Packed Computation of Exact Meaning Representations

13. Problem 1: Floating OperatorsNP VP V NP PP NP
Frank introduced Rachel to Patrick.
introduce-to(frank, rachel, patrick)
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Iddo Lev, Packed Computation of Exact Meaning Representations

14. Problem 1: Floating OperatorsNP VP V NP PP NP N’ RC VP
Det N VP NP
Frank introduced Rachel to every person who visited me that summer.
every(λx.person(x)visit(x,me), λx.introduce-to(frank, rachel, x))
every(P,Q) x. [P(x)  Q(x)]
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

15. Problem 1: Floating Operators
A brave sailor walked by.
a(λx.[sailor(x)brave(x)], λx.walk-by(x)) S NP N’ N VP
Adj
An occasional sailor walked by.
occasionally(a(λx.sailor(x), λx.walk-by(x))) S NP N’ N VP
Adj
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

16. Problem 2: More Than One Meaning
“In this country, a woman gives birth every 15 minutes. Our job is to find that woman, and stop her.”
-- Groucho Marx
every 15 minutes a woman gives birth
a woman every 15 minutes gives birth
You may not smoke.
You may not succeed.
All these books are not interesting.
All that glitters is not gold.
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

17. Iddo Lev, Packed Computation of Exact Meaning Representations
Glue Semantics
Glue Semantics:
A flexible framework for mapping syntax to semantics
Pieces of syntax correspond to pieces of semantics
Pieces of semantics combine with each other according to constraints
Like jigsaw puzzle, but possibly with more than one solution
Not a simple one-to-one mapping
References
Dalrymple et al. Semantics and Syntax in Lexical Functional Grammar Mary Dalrymple. Lexical Functional Grammar Asudeh, Crouch, Dalrymple. The syntax-semantics interface. 2002
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Iddo Lev, Packed Computation of Exact Meaning Representations

18. Iddo Lev, Packed Computation of Exact Meaning Representations
Glue Semantics
(simplified example) S NP VP NP
Name V
Name
statements
John
saw
Mary
mary
xy.see(x,y)
john
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Iddo Lev, Packed Computation of Exact Meaning Representations

19. Iddo Lev, Packed Computation of Exact Meaning Representations
Glue Semantics
(simplified example)
S a
b NP VP
NP c
Name V
Name
statements
John
saw
Mary
mary : c
xy.see(x,y) : b  c  a
john : b
prover
derivation
b b  c  a
c c  a a
john :
xy.saw(x,y) :
y.saw(john,y) :
mary :
saw(john,mary) :
gain: order of combination does not have to follow tree hierarchy
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

20. Problem 1: Floating OperatorsNP VP NP VP
λx.[sailor(x)brave(x)]
λQλR.occasionally[Q(λx.sailor(x),R)] N’ N’
Adj N
Adj N
A brave sailor walked by.
An occas. sailor walked by.
λPλR.a(P,R)
λx.sailor(x)
λx.walk-by(x)
λPλR.a(P,R)
λx.sailor(x)
λx.walk-by(x)
λPλx.[P(x)brave(x)]
λPλQλR.occasionally[Q(P,R)]
a(λx.[sailor(x)brave(x)], λx.walk-by(x))
occasionally[a(λx.sailor(x), λx.walk-by(x))]
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Iddo Lev, Packed Computation of Exact Meaning Representations

21. Iddo Lev, Packed Computation of Exact Meaning Representations
Glue Semantics
S a
Flexible handling of
floating operators.
b NP VP
N’ c
λPλR.a(P,R) : c  (b  a)  a
Adj N
An occas. sailor walked by.
λx.sailor(x) : c
λx.walk-by(x) : b  a
occasionally[a(λx.sailor(x), λx.walk-by(x))]
c c  (b  a)  a
b  a (b  a)  a
a a  a a
λS.occasionally[S] : a  a
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

22. Iddo Lev, Packed Computation of Exact Meaning Representations
Glue Semantics
(simplified example)
Can yield more than one meaning.
A woman gives birth every 15 minutes.
“gives birth” G : a
“a woman” A : a  a
“every 15 minutes” E : a  a
two possible derivations:
G : a A : a  a
A(G) : a E : a  a
E(A(G)) : a
G : a E : a  a
E(S) : a A : a  a
A(E(S)) : a
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

23. Glue Semantics Shared labels constrain how statements combine
“Resource Sensitive”: Use each statement exactly once
Inference rules:
Application
:A :AB
():B
Abstraction
[x:A]
:B
x.:AB
Linear Logic
(implicative fragment)
In Glue Semantics, can impose further constraints on combinations.
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

24. Iddo Lev, Packed Computation of Exact Meaning Representations
Outline 
 Motivation
 From Syntax to Semantics
 Packed Computation
 Conclusion 
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

25. Iddo Lev, Packed Computation of Exact Meaning Representations
Ambiguity
Flying planes can be dangerous. Therefore, only licensed pilots are allowed to do it.
Flying planes can be dangerous. Therefore, some people are afraid to ride in them.
We cannot always disambiguate the sentence just by looking at the sentence itself.
We sometimes need to take the larger context and information into account.
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Iddo Lev, Packed Computation of Exact Meaning Representations

26. Iddo Lev, Packed Computation of Exact Meaning Representations
Ambiguity
Alternatives multiply across layers…
Text
Morphology
Syntax
Semantics KR
Reasoning
… so we can’t keep all the alternatives separately
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Iddo Lev, Packed Computation of Exact Meaning Representations

27. Iddo Lev, Packed Computation of Exact Meaning Representations
Early Pruning
Select most likely analysis at each level X
Oops: Strong constraints may reject the so-far-best (and only) option
Statistics X X X
Text
Morphology
Syntax
Semantics KR
Reasoning
Locally less likely option but globally correct
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Iddo Lev, Packed Computation of Exact Meaning Representations

28. Packing The sheep liked the fish. More than one sheep?
More than one fish?
The sheep-sg liked the fish-sg.
The sheep-pl liked the fish-sg.
The sheep-sg liked the fish-pl.
The sheep-pl liked the fish-pl.
Options multiplied out
The sheep liked the fish
sg pl
Options packed
Packed representation:
Encodes all analyses without loss of information
Common items represented and computed just once
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

29. Iddo Lev, Packed Computation of Exact Meaning Representations
Packing
Calculate compactly all analyses at each stage
Push ambiguities through the stages
Possibly, filter and keep only N-best at each stage in a packed form (not only 1-best)
This approach is being pursued in the XLE system at PARC (and Powerset Inc.)
(Maxwell & Kaplan ’89,93,95)
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

30. Packing In Syntax: Chart Parser
A chart parser for a context-free grammar can compute an exponential number of parse trees in O(n3) time by representing and computing them compactly.
Instead of separately:
we have:
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Iddo Lev, Packed Computation of Exact Meaning Representations

31. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Structures
XLE manages natural language ambiguity by packing similar structures and managing them under a free-choice space
C-structure forest
Packed F-structure
Choice Space:
true  A1  A2
A1  A2  false
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

32. Currently in XLE : : Text morph. C-str F-str MR KR answer
semantic rewrite rules
FST
morph.
glue spec.
glue prover
parser
unpack
F-str1
Glue1
MR1
pack : :
C-str
F-str MR KR
C-F
F-strn
Gluen
MRn
answer
= packed
= packed calculation + possibly filter N-best
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

33. Iddo Lev, Packed Computation of Exact Meaning Representations
The Goal
Text
FST
morph.
parser
Glue statements
C-str
F-str MR KR
glue spec.
glue prover
C-F
answer
= packed
= packed calculation + possibly filter N-best
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Iddo Lev, Packed Computation of Exact Meaning Representations

34. Goal: Packed Meaning Representation
Bill saw the girl with the telescope.
a:1 e. see(e)  agent(e,bill)  theme(e,the(x.girl(x))  with(e,the(y.tele(y)))
a:2 e. see(e)  agent(e,bill)  theme(e, the(x. girl(x)  with(x,the(y.tele(y))) )
e. see(e)  agent(e,bill)  ●
girl(x)
theme(e, the(x. ● ))
●●
with(●,the(y.tele(y)))
x e
packed meaning representation
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Iddo Lev, Packed Computation of Exact Meaning Representations

35. Iddo Lev, Packed Computation of Exact Meaning Representations
Glue Specification
Glue specification – connecting syntactic and semantic pieces
NTYPE(f, NAME), PRED(f, p)  p : f
NTYPE(f, COMMON), PRED(f, p)  λx.p(x) : fv  fr
F-Structure
glue statements
john : a
λx.cake(x) : bv  br
“John ate the cake.”
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

36. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Glue Input
Packed F-structure
NTYPE(f, NAME), PRED(f, p)  p : f e
Glue specification
{1} e.see(e) : aveart
{2} P.e.P(e) : (aveart)at
{3} bill : be {4} xPe.P(e)agent(e,x) : be(aveart)(aveart)
{5} P.the(P) : (gvegrt)ge
{6} x.girl(x) : gvegrt {7} xPe.P(e)theme(e,x) : ge(aveart)(aveart)
{8} P.the(P) : (hvehrt)he
{9} x.tele(x) : hvehrt
{10} A1: yPe.P(e)with(e,y) : he(aveart)(aveart)
{11} A2: yPx.P(x)with(x,y) : he(gvegrt)(gvegrt)
“Bill saw the girl with the telescope.”
This combines
Glue Semantics
+ packing
at the input level 
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

37. Non-packed Prover (Hepple’96)
Rule:
Input:
 : A | S  : AB | S2
() : B | S1  S2
f : c c d q : c r : c
provided S1  S2 = 
Chart:
meaning
category
span f
c c d
{1} q c
{2} r
f(q)
cd
{3}
{1,2}
f(r)
{1,3}
f(q,r) d
{1,2,3}
f(r,q)
cannot combine:
{2}{1,2}  
complete derivation
(all indices were used)
Output:
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Iddo Lev, Packed Computation of Exact Meaning Representations

38. Iddo Lev, Packed Computation of Exact Meaning Representations
Syntactic Ambiguity
“Time flies like an arrow. Fruit-flies like a banana.”
-- Groucho Marx
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Iddo Lev, Packed Computation of Exact Meaning Representations

39. Naive Packed Algorithm
A1: [[John]a thinks that [[time]d flies [like [an arrow]c]]b]g
A2: [[John]a thinks that [[time flies]f like [an arrow]c]b]g
The chart algorithm will discover one history for [[time]d flies [like [an arrow]c]]b under A1
It may then continue under A1 with “John thinks that”
It will later discover a history for [[time flies]f like [an arrow]c]b under A2
So it will have to redo the work for “John thinks that” under A2
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Iddo Lev, Packed Computation of Exact Meaning Representations

40. Iddo Lev, Packed Computation of Exact Meaning Representations
Non-Packed Prover
Forget about meaning terms for now
(can reconstruct them after the derivation finishes)
Combine histories according to topological order of category graph
{2} {3}
{1}
{4}
{5}
{6}
category graph a
ab
ac b c
bcd
cd d
df f
mean.
category
span q
ab
{1} p a
{2} r s
ac
{3}
{4} t
bcd
{5} u
df
{6}
{1,2} {1,3}
{2,4} {3,4}
{1,2,5} {1,3,5}
t(q(p),s(r))
t(q(r),s(p))
{1,2,3,4,5}
{1,2,3,4,5,6}
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Iddo Lev, Packed Computation of Exact Meaning Representations

41. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
(Simplified example)
A1: [[John]a thinks that [[time]d flies [like [an arrow]c]]b]g
A2: [[John]a thinks that [[time flies]f like [an arrow]c]b]g
premises
choice
john a
{1} 1
think
abg
{2}
anarrow c
{3}
time d
{4} A1
fly
deb
{5}
like
ce
{6}
timeflies f
{7} A2
fcb
{8}
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

42. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
(Simplified example)
A1: [[John]a thinks that [[time]d flies [like [an arrow]c]]b]g
A2: [[John]a thinks that [[time flies]f like [an arrow]c]b]g
premises
choice
john a
{jn} 1
think
abg
{th}
anarrow c
{ar}
time d
{t} A1
fly
deb
{f}
like
ce
{k1}
timeflies f
{tf} A2
fcb
{k2}
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Iddo Lev, Packed Computation of Exact Meaning Representations

43. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
 Imagine how each derivation works separately; then figure out how to pack.
premises
choice
john a
{jn} 1
think
abg
{th}
anarrow c
{ar}
time d
{t} A1
fly
deb
{f}
like
ce
{k1}
timeflies f
{tf} A2
fcb
{lk2}
{f}
{t}
{k1}
{ar}
{k1,ar}
{th}
{jn}
{t,f}
{t,f,k1,ar}
{jn,th}
{jn,th,t,f,k1,ar}
Category graph
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Iddo Lev, Packed Computation of Exact Meaning Representations

44. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
 Imagine how each derivation works separately; then figure out how to pack.
{tf}
{k2}
premises
choice
john a
{jn} 1
think
abg
{th}
anarrow c
{ar}
time d
{t} A1
fly
deb
{f}
like
ce
{lk1}
timeflies f
{tf} A2
fcb
{k2}
{ar}
{tf,k2}
{tf,k2,ar}
{th}
{jn}
{jn,th}
{jn,th,tf,k2,ar}
Category graph
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

45. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
 Imagine how each derivation works separately; then figure out how to pack.
{tf}
{k2}
premises
choice
john a
{j} 1
think
abg
{th}
anarrow c
{a}
time d
{t} A1
fly
deb
{f}
like
ce
{k1}
timeflies f
{tf} A2
fcb
{k2}
{f}
{t}
{k1}
{ar}
{tf,k2}
{k1,ar}
{th}
{jn}
{t,f}
A2:{tf,k2,ar}
A1:{t, f,k1,ar}
{jn,th}
1:{ar} A1:{t, f,k1} A2:{tf,k2}
{jn,th,t,f,k1,ar}
{jn,th,tf,k2,ar}
1:{jn,th,ar} A1:{t, f,k1} A2:{tf,k2}
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

46. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
only possible in A1
history
under A1
under A2
packed span h1
{ar}
1:{ar} h2
{k1,ar}
A1:{k1,ar} h3
{t,f}
A1:{t,f} h4
{t,f,k1,ar}
A1:{t,f,k1,ar} h5
{tf,k2}
A2:{tf,k2} h6
{tf,k2,ar}
A2:{tf,k2,ar} h7
1:{ar} A1:{t,f,k1} A2:{tf,k2} h8
{jn,th}
1:{jn,th} h9
{jn,th,t,f,k1,ar}
{jn,thtf,k2,ar}
1:{jn,th,ar} A1:{t,f,k1} A2:{tf,k2}
packed common part
{tf}
{k2}
{f}
{t}
{k1}
{ar}
{tf,k2}
{k1,ar}
{t,f}
A2:{tf,k2,ar}
{jn}
{th}
A1:{t, f,k1,ar}
{jn,th}
1:{ar} A1:{t, f,k1} A2:{tf,k2}
1:{jn,th,ar} A1:{t, f,k1} A2:{tf,k2}
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

47. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
Two histories with categories A and AB can be combined:
original algorithm: if their spans are disjoint
packed algorithm: can combine them in all contexts in which
their spans are disjoint
original combination:
provided S1  S2 = 
and S = S1  S2
A | S AB | S2
B | S
packed combination:
provided C1  C2  0
and combinable(PS1, PS2, C)
and PS = union(C, PS1, PS2)
C1 | A | PS C2 | AB | PS2
C | B | PS
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

48. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
Two histories with categories A and AB can be combined:
original algorithm: if their spans are disjoint
packed algorithm: can combine them in all contexts in which
their spans are disjoint
packed combination:
provided C1  C2  0
and combinable(PS1, PS2, C)
and PS = union(C, PS1, PS2)
C1 | A | PS C2 | AB | PS2
C | B | PS
combinable: 1:{3,4} 1:{5,6,7}
combinable: 1:{3},A1:{6,7} 1:{4,5},A2:{6,8}
combinable: A1:{6},A2:{7}  A1:{6},A2:{8}
non-combinable: 1:{4},A1:{6} 1:{5,6},A2:{4} (6 is in A1 in both, 4 is in A2 in both)
 1:{3,4,5,6,7}
 1:{3,4,5,6},A1:{7},A2:{8}
 A2:{7,8}
A1:{4,6} A2:{4}
A1:{5,6} A2:{4,5,6}
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

49. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
Two histories with the same category can be packed:
original algorithm: if their spans are identical
packed algorithm: if their spans are identical in the shared contexts
can pack: 1:{3,4,5} 1:{3,4,5}
can pack: A1:{1},A2:{2} A2:{2},A3:{3}
can pack: A1:{t,f,k1,ar} A2:{tf,k2,ar}
cannot pack: 1:{5},A1:{6} 1:{5},A2:{7} ({5,6}{5} in A1 , {5}{5,7} in A2))
 1:{3,4,5}
 A1:{1},A2:{2},A3:{3}
 1:{ar}, A1:{t,f,k1}, A2:{tf,k2}
A1:{5,6} A2:{5}
A1:{5} A2:{5,7}
A2:{tf,k2,ar}
A1:{t, f,k1,ar}
1:{ar} A1:{t, f,k1} A2:{tf,k2}
{ar}
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

50. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
Reconstruction of packed meaning representation:
history
packed span
meaning h1
1:{ar}
l1 : anarrow h2
A1:{k1,ar}
like(l1) h3
A1:{t,f}
fly(time) h4
A1:{t,f,k1,ar}
fly(time,like(l1)) h5
A2:{tf,k2}
like(timeflies) h6
A2:{tf,k2,ar}
like(timeflies,l1) h7
1:{ar} A1:{t,f,k1} A2:{tf,k2}
A1:fly(time,like(l1)) A2:like(timeflies,l1) h8
1:{jn,th}
think(john) h9
1:{jn,th,ar} A1:{t,f,k1} A2:{tf,k2}
think(john, ●)
anarrow
fly(time,like(●))
like(timeflies,●) A1 A2
category graph
packed meaning representation
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

51. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
What if the category graph has cycles?
Calculate strongly connected components (SCCs) and the induced directed-acyclic graph (DAG) (+ topological sort)
In each SCC, run basic algorithm to find all possibilities
If SCC is simple (X, XX) then optimize: use as much material as possible before moving out of the cycle
{2} {3} {4}
{1}
XX X
{1} {1,2} {1,3} {1,4} {1,2,3} {1,2,4} {1,3,4} {1,2,3,4}
category graph
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

52. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
[girl [with the telescope]]A2
A2:{wt}
1:{grl}
XX X
1:{grl} A1:{grl} A2:{grl,wt} 1:{grl}, A2:{wt}
category graph
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

53. Iddo Lev, Packed Computation of Exact Meaning Representations
Packed Derivation
Category graph
{1} e.see(e) : aveart
{2} P.e.P(e) : (aveart)at
{3} bill : be {4} xPe.P(e)agent(e,x) : be(aveart)(aveart)
{5} P.the(P) : (gvegrt)ge
{6} x.girl(x) : gvegrt {7} xPe.P(e)theme(e,x) : ge(aveart)(aveart)
{8} P.the(P) : (hvehrt)he
{9} x.tele(x) : hvehrt
{10} A1: yPe.P(e)with(e,y) : he(aveart)(aveart)
{11} A2: yPx.P(x)with(x,y) : he(gvegrt)(gvegrt)
1:{8}
1:{9}
(hvehrt)he
hvehrt
A2:{11}
he(gvegrt)(gvegrt) he
1:{8,9}
A2:{8,9,11}
(gvegrt)(gvegrt)
(gvegrt)ge
gvegrt
1:{6},A2:{8,9,11}
packing in a cycle
A1:{10} ge
geaetaet
1:{3}
heaetaet
beaetaet be
Need to calculate strongly-connected components before topological sort.
A1:{8,9,10}
1:{5,6,7}, A2:{8,9,11}
1:{3,4}
aetaet
1:{2}
aetat
aet
1:{1,3,4,5,6,7,8,9}, A1:{10},A2:{11} at
1:{1,2,3,4,5,6,7,8,9}, A1:{10},A2:{11}
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

54. Iddo Lev, Packed Computation of Exact Meaning Representations
Outline 
 Motivation
 From Syntax to Semantics
 Packed Computation
 Conclusion  
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

55. Iddo Lev, Packed Computation of Exact Meaning Representations
My Dissertation
How to map syntactic analysis to meaning representations
How to compute all meaning representations efficiently
Linguistic analysis of advanced NL constructions using the above framework
anaphora (interaction with truth conditions)
comparatives
reciprocals (each other, one another)
same/different
How to translate meaning representations to inference representations (FOL)
Focus of this talk
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

56. Iddo Lev, Packed Computation of Exact Meaning Representations
Summary
Mapping syntax to exact meaning representations using Glue Semantics
More powerful than traditional approach
Easier for users, more principled than semantic rewrite rules
Covered advanced NL constructions
Computing all meaning representations efficiently
Input: packed syntactic analysis
Output: packed meaning representation
 Pushing packed ambiguities through the semantics stage
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

57. Iddo Lev, Packed Computation of Exact Meaning Representations
Future Work
Researchers can use this work as a basis
Use this in applications
Logic puzzles, word problems, NLIDB, regulation texts
Extend this approach to additional NL constructions
(requires some linguistic research)
Extend idea of packing to anaphora/plurality and back-end inference stages
Some initial work on packed reasoning at PARC
Extend statistical disambiguation to packed semantic structures
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations

58. Iddo Lev, Packed Computation of Exact Meaning Representations
Thanks
Stanley Peters
Dick Crouch
Chris Manning
Mike Genesereth
Johan van Benthem
NLTT group at PARC
Ivan Sag
Bill MacCartney, Mihaela Enachescu, Powerset Inc.
Beth Nowadnick
April 17, 2007
Iddo Lev, Packed Computation of Exact Meaning Representations