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


Natural Language Understanding

• How can we improve accuracy?• Let’s take it for a moment to the

extreme– Exact NLU applications


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.


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:


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


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


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


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


• 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


Outline



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)


Problem 1: Floating Operators

Frank introduced Rachel to Patrick.

introduce-to(frank, rachel, patrick)

S

NP

PP

VP

V

NP

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))

S

NPVPVP

RCN’

N

NP

Det

PP

VP

V

NP

NP

every(P,Q) x. [P(x) Q(x)]



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


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.


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


Glue Semantics

statements

mary xy.see(x,y) john

John saw Mary

Name

NP

Name

NP

V

VPS

(simplified example)


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) :



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))]


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.


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)


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.


Outline



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.


Ambiguity

Alternatives multiply across layers…

Morphology

Syntax

Sem

antics

KR

Reasoning

… so we can’t keep all the alternatives separately

Text


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


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


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)


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.


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


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


The Goal

morph.

C-str F-str KR

answer

parser

C-F

Text

FST

MRGlue

statementsgluespec.

glueprover

= packed calculation + possibly filter N-best

= packed


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


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.”


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


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:


Syntactic Ambiguity

“Time flies like an arrow. Fruit-flies like a banana.”

-- Groucho Marx


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


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


Packed Derivation

• (Simplified example)



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}


Packed Derivation

• (Simplified example)



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}


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}


Packed Derivation

Category graph


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}


Packed Derivation


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}


{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}


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


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}


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}


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


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


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


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}


Outline



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


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


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


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

packed computation of exact meaning representations iddo lev department of computer science stanford...

Documents

x exact meaning representation

sculptures e

exact nlu tasks

text slide

sculptures d

sculptures c

extreme exact nlu applications

dthree sculptures