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Transcript of Packed Computation of Exact Meaning Representations Iddo Lev Department of Computer Science Stanford...
Packed Computation of Exact Meaning
Representations
Iddo Lev Department of Computer Science
Stanford University
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 2
Outline
Motivation From Syntax to Semantics Packed Computation Conclusion
Motivation
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
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
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
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
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 toinference representations (FOL)
Focus of this talk
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 10
• 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}, xy.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).
Structural Semantics Challenges
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 11
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
barksλz. bark(z)
Detevery
λP.λR. x. [P(x) R(x)]
Noundog
λy.dog(y)
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 13
Problem 1: Floating Operators
Frank introduced Rachel to Patrick.
introduce-to(frank, rachel, patrick)
S
NP
PP
VP
V
NP
NP
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 14
Problem 1: Floating Operators
Frank introduced Rachel to every person who visited me that summer.
every(λx.person(x)visit(x,me), λx.introduce-to(frank, rachel, x))
S
NPVPVP
RCN’
N
NP
Det
PP
VP
V
NP
NP
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
AdjAn 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
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. 1999Mary Dalrymple. Lexical Functional Grammar. 2001Asudeh, Crouch, Dalrymple. The syntax-semantics interface. 2002
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 18
Glue Semantics
statements
mary xy.see(x,y) john
John saw Mary
Name
NP
Name
NP
V
VPS
(simplified example)
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 19
Glue Semantics
prover
statements
mary : cxy.see(x,y) : b c ajohn : b
John saw Mary
Name
b NP
Name
NP cV
VPS a
derivation
b b c a
c c a
a gain: order of combination does not have to follow tree hierarchy
(simplified example)
john : xy.saw(x,y) :
y.saw(john,y) :mary :
saw(john,mary) :
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 20
Problem 1: Floating Operators
A brave sailor walked by.
S
NP VP
N’
NAdj
λPλR.a(P,R)
λPλx.[P(x)brave(x)]
λx.sailor(x) λx.walk-by(x)
λx.[sailor(x)brave(x)]
An occas. sailor walked by.
S
NP VP
N’
NAdj
λPλR.a(P,R)
λPλQλR.occasionally[Q(P,R)]
λx.sailor(x) λx.walk-by(x)
λQλR.occasionally[Q(λx.sailor(x),R)]
a(λx.[sailor(x)brave(x)], λx.walk-by(x))
occasionally[a(λx.sailor(x), λx.walk-by(x))]
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 21
Glue Semantics
An occas. sailor walked by.
S a
b NP VP
N’ c
NAdjλPλR.a(P,R) : c (b a) a
λS.occasionally[S] : a a
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
Flexible handling of floating operators.
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 22
Glue Semantics
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
Can yield more than one meaning.(simplified example)
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 :AB():B
Abstraction
[x:A]¦
:B x.:AB 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
Outline
Motivation From Syntax to Semantics Packed Computation Conclusion
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 25
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.
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 26
Ambiguity
Alternatives multiply across layers…
Morphology
Syntax
Sem
antics
KR
Reasoning
… so we can’t keep all the alternatives separately
Text
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 27
Early Pruning
• Select most likely analysis at each level
X
• Oops: Strong constraints may reject the so-far-best (and only) option
Morphology
Syntax
Sem
antics
KR
Reasoning
X
X
Statistics
X
Locally less likely option but globally correct
Text
April 17, 2007 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 sgpl
sgpl
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
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
Instead of separately:
we have:
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.
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 31
Packed Structures
C-structure forest Packed F-structure
true A1 A2
A1 A2 false
Choice Space:
XLE manages natural language ambiguity by packing similar structures and managing them under a free-choice space
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 32
Currently in XLE
morph.
C-str F-str KR
answer
parser
C-F
Text
FST
unpack F-str1
F-strn
Glue1
Gluen
::
MR1
MRn
MR::
gluespec.
glueprover
pack
semantic rewrite rules
= packed calculation + possibly filter N-best
= packed
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 33
The Goal
morph.
C-str F-str KR
answer
parser
C-F
Text
FST
MRGlue
statementsgluespec.
glueprover
= packed calculation + possibly filter N-best
= packed
April 17, 2007 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
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 35
Glue Specification
F-Structure
Glue specification – connecting syntactic and semantic pieces
NTYPE(f, NAME), PRED(f, p) p : f
glue statements
john : a
NTYPE(f, COMMON), PRED(f, p) λx.p(x) : fv fr
λx.cake(x) : bv br
“John ate the cake.”
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 36
Packed Glue Input
Glue specification
{1} e.see(e) : avear
t
{2} P.e.P(e) : (avear
t)at
{3} bill : be
{4} xPe.P(e)agent(e,x) : be(avear
t)(avear
t){5} P.the(P) : (gv
egrt)ge
{6} x.girl(x) : gvegr
t
{7} xPe.P(e)theme(e,x) : ge(avear
t)(avear
t){8} P.the(P) : (hv
ehrt)he
{9} x.tele(x) : hvehr
t
{10} A1: yPe.P(e)with(e,y) : he(avear
t)(avear
t){11} A2: yPx.P(x)with(x,y) : he(gv
egrt)(gv
egrt)
This combines Glue Semantics + packingat the input level
NTYPE(f, NAME), PRED(f, p) p : f e
“Bill saw the girl with the telescope.”
Packed F-structure
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 37
Non-packed Prover (Hepple’96)
meaning category spanf c c d {1}q c {2}r
f(q)
c
cd
{3}
{1,2}f(r) cd {1,3}
f(q,r) d {1,2,3}f(r,q) d {1,2,3}
f : c c d q : c r : c
Input:
Chart:
cannot combine:{2}{1,2}
complete derivation(all indices were used)Output:
provided S1 S2 =
: A | S1 : AB | S2
() : B | S1 S2
Rule:
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 38
Syntactic Ambiguity
“Time flies like an arrow. Fruit-flies like a banana.”
-- Groucho Marx
April 17, 2007 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
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 40
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
mean. category span
q ab {1}
p a {2}
r
s
a
ac
{3}
{4}
t bcd {5}
u df {6}
{2,4} {3,4}
{1,2} {1,3}
{1,2,5} {1,3,5}
{1,2,3,4,5}
t(q(r),s(p))t(q(p),s(r))
{1,2,3,4,5,6}
{2} {3}{1} {4}
{5}
{6}
category graph
aab ac
b cbcd
cd
d
df
f
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 41
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 abg {2}
anarrow c {3}
time d {4} A1
fly deb {5}
like ce {6}
timeflies f {7} A2
like fcb {8}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 42
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 abg {th}
anarrow c {ar}
time d {t} A1
fly deb {f}
like ce {k1}
timeflies f {tf} A2
like fcb {k2}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 43
Packed Derivation
Category graph
Imagine how each derivation works separately; then figure out how to pack.
premises choice
john a {jn} 1
think abg {th}
anarrow c {ar}
time d {t} A1
fly deb {f}
like ce {k1}
timeflies f {tf} A2
like fcb {lk2}
{th}
{jn,th}
{t}{f}
{t,f}
{k1,ar}
{t,f,k1,ar}
{jn,th,t,f,k1,ar}
{ar}{k1}
{jn}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 44
Packed Derivation
Category graph
Imagine how each derivation works separately; then figure out how to pack.
premises choice
john a {jn} 1
think abg {th}
anarrow c {ar}
time d {t} A1
fly deb {f}
like ce {lk1}
timeflies f {tf} A2
like fcb {k2}
{th}
{jn,th}
{ar}
{tf} {k2}
{tf,k2}
{jn,th,tf,k2,ar}
{tf,k2,ar}
{jn}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 45
Packed Derivation
Imagine how each derivation works separately; then figure out how to pack.
premises choice
john a {j} 1
think abg {th}
anarrow c {a}
time d {t} A1
fly deb {f}
like ce {k1}
timeflies f {tf} A2
like fcb {k2}
{jn} {th}
{jn,th}
{ar}
{tf} {k2}
A2:{tf,k2,ar}
{tf,k2}{k1}{t}{f}
{t,f}
A1:{t, f,k1,ar}
{jn,th,t,f,k1,ar}
{k1,ar}
{jn,th,tf,k2,ar}
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 46
{jn}{th}
{jn,th}
{ar}
{tf} {k2}
A2:{tf,k2,ar}
{tf,k2}{k1}{t}{f}
{t,f}
A1:{t, f,k1,ar}
{k1,ar}
1:{ar} A1:{t, f,k1} A2:{tf,k2}
1:{jn,th,ar} A1:{t, f,k1} A2:{tf,k2}
Packed Derivation
only possible in A1
packed common part
history under A1 under A2 packed spanh1 {ar} {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 {t,f,k1,ar} {tf,k2,ar} 1:{ar} A1:{t,f,k1} A2:{tf,k2}h8 {jn,th} {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}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 47
Packed Derivation
• Two histories with categories A and AB 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 | S1 AB | S2
B | S
packed combination: provided C1 C2 0and combinable(PS1, PS2, C)and PS = union(C, PS1, PS2)
C1 | A | PS1 C2 | AB | PS2
C | B | PS
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 48
Packed Derivation
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}
A1:{4,6} A2:{4}
A2:{7,8}
packed combination: provided C1 C2 0and combinable(PS1, PS2, C)and PS = union(C, PS1, PS2)
C1 | A | PS1 C2 | AB | PS2
C | B | PS
• Two histories with categories A and AB can be combined:– original algorithm: if their spans are disjoint– packed algorithm: can combine them in all contexts in which
their spans are disjoint
A1:{5,6} A2:{4,5,6}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 49
A2:{tf,k2,ar}A1:{t, f,k1,ar}
1:{ar} A1:{t, f,k1} A2:{tf,k2}
{ar}
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}
1:{ar}, A1:{t,f,k1}, A2:{tf,k2}
A1:{5,6} A2:{5} A1:{5} A2:{5,7}
A1:{1},A2:{2},A3:{3}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 50
Packed Derivation
think(john, ●)
anarrow
fly(time,like(●)) like(timeflies,●)A1 A2
history packed span meaningh1 1:{ar} l1 : anarrowh2 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}
Reconstruction of packed meaning representation:
packed meaning representationcategory graph
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 51
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, XX) then optimize:
use as much material as possible before moving out of the cycle
XX
X
{1}{2} {3} {4}
{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
Packed Derivation
XX
X
1:{grl}A2:{wt}
1:{grl} A1:{grl} A2:{grl,wt}1:{grl}, A2:{wt}
category graph
[girl [with the telescope]]A2
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 53
Packed Derivation
be
aetaet
aetaetat
at
(gvegr
t)gegv
egrt
ge geaetaet
(hvehr
t)he hvehr
t
(gvegr
t)(gvegr
t)
he(gvegr
t)(gvegr
t)he
heaetaet
1:{9}
A2:{11}
A2:{8,9,11}
1:{6},A2:{8,9,11}
A1:{10}
A1:{8,9,10}
beaetaet
1:{1,3,4,5,6,7,8,9}, A1:{10},A2:{11}
Category graph
Need to calculate strongly-connected components before topological sort.
1:{5,6,7}, A2:{8,9,11}
1:{1,2,3,4,5,6,7,8,9}, A1:{10},A2:{11}
1:{8}
1:{8,9}
1:{3,4}
1:{2}
packing in a cycle
{1} e.see(e) : avear
t
{2} P.e.P(e) : (avear
t)at
{3} bill : be
{4} xPe.P(e)agent(e,x) : be(avear
t)(avear
t){5} P.the(P) : (gv
egrt)ge
{6} x.girl(x) : gvegr
t
{7} xPe.P(e)theme(e,x) : ge(avear
t)(avear
t){8} P.the(P) : (hv
ehrt)he
{9} x.tele(x) : hvehr
t
{10} A1: yPe.P(e)with(e,y) : he(avear
t)(avear
t){11} A2: yPx.P(x)with(x,y) : he(gv
egrt)(gv
egrt)
1:{3}
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 54
Outline
Motivation From Syntax to Semantics Packed Computation Conclusion
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 55
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 toinference representations (FOL)
Focus of this talk
April 17, 2007 Iddo Lev, Packed Computation of Exact Meaning Representations 56
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
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
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