Executable Semantic Parsing

Executable Semantic Parsing

ESSLLI

Class 2

Instructor: Jonathan Berant

Class 1 reminder

We learned to manually write down logical forms for various naturallanguage constructs

• Entities

• Relations

• Superlatives

• Events

• · · ·

But how do we build logical forms automatically?

1

Outline

• Compositionality

– Grammars and derivations

– Example

– Lexicon

– Modeling

– CCG

– Exercise

2

Outline



– Example

– Lexicon

– Modeling

– CCG

– Exercise

3

Grammars and derivations

Simple grammar

(lexicon) Set ⇒ Phrase Chicago ⇒ Chicago

(lexicon) Binary⇒ Phrase PlacesLived⇒ lived in

(join) Set ⇒ Binary Set b.s ⇒ b s

(intersect) Root ⇒ Set Set s1 u s2 ⇒ s1 s2

4

Grammars and derivations

Simple grammar





Type.PersonuPlaceLived.Chicago

Type.Person

people

who PlaceLived.Chicago

PlaceLived

lived in

Chicago

Chicago

lexicon

lexiconlexicon

join

intersect

4

Grammar

Simple grammar





A grammar G is a 4-tuple:

V: chicago, live in

N : Binary,Set,Root

Root ∈ N : start symbol

R: grammar rules

5

Grammar rules

Simple grammar





A rule r ∈ R has:

A ∈ N : left-hand-side (LHS) non-terminal

α ∈ (N ∪ V)+ right-hand-side

f semantic function for building derivations

Semantic functions are the key component!

6

Derivation

Root:Type.CityuPlaceOfBirthOf.AbeLincoln

what Set:Type.City

city

was Set:PlaceOfBirthOf.AbeLincoln

Entity:AbeLincoln

abraham lincoln

Binary:PlaceOfBirthOf

born in

A derivation tree dAi:j over a span x = (wi, . . . , wj−1):

Spans (wi, . . . , wj−1)

Has category d.c = A ∈ NHas logical form d.z

Has children that are derivations or terminals

7

Semantic functions

A function f : Dk → 2D

Example:

• r = A→ B C [f ]

• DAi:j = f(dBi:k, d

Ck:j)

Lexicon function:

Lex( lincoln ) =

{ Entity:AbeLincoln

lincoln

,

Entity:LincolnFilm

lincoln

, ...

}

8

Semantic functions

Join function:

Join

(Entity:AbeLincoln

abraham lincoln,Binary:PlaceOfBirthOf

born

)=

{ Set:PlaceOfBirthOf.AbeLincoln

Entity:AbeLincoln

abraham lincoln

Binary:PlaceOfBirthOf

born

}

Merge function:

Intersect

( Set:Type.City

city,Set:ReleaseDateOf.LincolnFilm

abraham lincoln born

)= {}

Return sets (unlike CFGs)

9

Semantic function

IdentityFn Copy logical form

SelectFn Select one child logical form

DateFn Convert date descriptions to date

FilterPosFn Filter words by POS

10

Semantic function





ContextFn Integrate arbitrary context

What city was abraham lincoln born?

How about his wife?

10

Semantic function





ContextFn Integrate arbitrary context

What city was abraham lincoln born?

How about his wife?

Flexible! arbitrary logic can be used

λx.Border(x, Italy)

S \Nbordering Italy

⇒λy.λx.Border(x, y) Italy

(S \N)/N N

bordering Italy

10

Outline



– Example

– Lexicon

– Modeling

– CCG

– Exercise

11

Example

./run @mode=simple-lambdadcs \

-Grammar.inPaths esslli 2016/class2 demo.grammar \

-SimpleLexicon.inPaths esslli 2016/class2 demo.lexicon

12

Example

california

the golden state

cities in the golden state

towns located in california

rivers bordering california

13

Example

california

the golden state

cities in the golden state

towns located in california

rivers bordering california

Is the last utterance meaningful?

How can we avoid such logical forms?

13

Outline



– Example

– Lexicon

– Modeling

– CCG

– Exercise

14

The lexicon problem

california California

the golden state California

cities Type.Citytown

towns Type.CityTown

in ContainedBy

How is the lexicon generated?

15

The lexicon problem

california California

the golden state California

cities Type.Citytown

towns Type.CityTown

in ContainedBy

How is the lexicon generated?

• Annotation

• Exhaustive search

• String matching

• Supervised alignment

• Unsupervised alginment

• Learning

15

Annotation

where Type.Location

most λx.λy.argmax(y, x)

how many λx.count(x)

Useful for function words

16

Annotation

where Type.Location




city Type.CityTown

lake Type.Lake

area Area

Useful for small domains

16

Annotation

where Type.Location




city Type.CityTown

lake Type.Lake

area Area

Useful for small domains

Large domains? Different languages?

16

Exhaustive search

city Type.Lake

state Population

people Area

area λx.count(x)

how many Type.CityTown

. . . . . .

17

Exhaustive search

city Type.Lake

state Population

people Area

area λx.count(x)


. . . . . .

Size of lexicon: |V| × |L|

Intractable for large domains

17

Exhaustive search

city Type.Lake

state Population

people Area

area λx.count(x)


. . . . . .

Size of lexicon: |V| × |L|

Intractable for large domains

Exhaustive?

actress Profession.Actor uGender.Female

relative λx.Parent.x t Sibling.x tChild.x

expat µx.BirthPlaceOf.x 6= argmax(x,PlacesLived)

17

String match

Knowledge-bases often have language descriptions

area Area

• Language specific

• Limited coverage and noisy

18

String match

Knowledge-bases often have language descriptions

area Area

• Language specific

• Limited coverage and noisy

• Useful as a feature at training time

18

Supervised alignment

Assume access to (x, z) language-logical form pairs

State with the largest area

argmax(Type.State,Area)

19





Define patterns over (x, z) to generate candidate lexicon entries

State

with the largest

largest

area

State

Type.State

λx.Type.x

Area

λx.λy.Argmax(x, y)

19






State

with the largest

largest

area

State

Type.State

λx.Type.x

Area


Keep counts for each lexical entry as a feature

19






State

with the largest

largest

area

State

Type.State

λx.Type.x

Area


Keep counts for each lexical entry as a feature

Predefined patterns

Generalization? 19

Unsupervised alignment

(Barack Obama, was born in, Honolulu)

(Albert Einstein, was born in, Ulm)

(Barack Obama, lived in, Chicago)

... 15M triples ...

BarackObama

Person

Type

Politician

Profession

1961.08.04

DateOfBirth

HonoluluPlaceOfBirth

Hawaii

ContainedBy

City

Type

UnitedStates

ContainedBy

USState

Type

Event8

Marriage

MichelleObama

Spouse

Type

FemaleGender

1992.10.03

StartDate

Event3

PlacesLived

Chicago

Location

Event21

PlacesLived

Location

ContainedBy

(BarackObama, HasBirthplace, Honolulu)

(Albert Einstein, HasBirthplace, Ulm)

(BarackObama, PlacesLived.Location, Chicago)

... 600M triples ...

B et al., 2013

20


grew up in[Person,Location]

born in[Person,Date]

married in[Person,Date]

born in[Person,Location]

DateOfBirth

PlaceOfBirth

Marriage.StartDate

PlacesLived.Location

(BarackObama,Honolulu)

(MichelleObama,Chicago)

(RandomPerson,Seattle) (BarackObama,Chicago)

21






DateOfBirth

PlaceOfBirth

Marriage.StartDate





Alignment features

phrase-count:15,765

intersection-count: 6,048

21






DateOfBirth

PlaceOfBirth

Marriage.StartDate





Alignment features

phrase-count:15,765

intersection-count: 6,048

Generalizes to test set

Restricted domain21

Advanced

• Change lexicon at training time

• batch voting

• Generative models

[Kwiatkowski et al., 2010; Kwiatkowski et al. 2011; Artzi et al., 2014;Krishnamurthy, 2015]

22

Outline



– Example

– Lexicon

– Modeling

– CCG

– Exercise

23

Bridging/trace predicates

Problem: Language defines semantics implicitly

Italy’s language Type.Language u LanguageOf.Italy

Where is Beijing Type.Location u Contains.Beijing

Boston flight Type.Flight u To.Boston

24

Bridging/trace predicates

Problem: Language defines semantics implicitly

Italy’s language Type.Language u LanguageOf.Italy

Where is Beijing Type.Location u Contains.Beijing

Boston flight Type.Flight u To.Boston

Lexicon?

’s LanguageOf

is Contains

??? To

24

Naive solution

language Type.Language

language LanguageOf

where Type.Location

where Contains

flight Type.Filght

flight To

flight From

More pressure on lexicon learning

25

Naive solution

language Type.Language

language LanguageOf

where Type.Location

where Contains

flight Type.Filght

flight To

flight From

More pressure on lexicon learning

Infer missing predicates from context

Can be implemented as a semantic function! (BridgeFn)

25

Bridging 1: two unaries

Boston

Type.Flight

boston flight

lex

lex

26


Boston

To

Type.Flight

boston flight

lex

lex

bridging

Type.Flight u To.Boston

Insert any type-matching binary

(bridge first) Set ⇒ Set Set

26


Boston

From

Type.Flight

boston flight

lex

lex

bridging

Type.Flight u To.Boston


(bridge first) Set ⇒ Set Set

Learn to choose implicit predicate 26

Bridging 2: single unary

Beijing

Where is Beijing

lex

27

Bridging 2: single unary

Contains

Beijing

Where is Beijing

lex

bridging


Contains.Beijing

(bridge) Set ⇒ Set

More uncertainty

27

Bridging 3: n-ary relations

Marriage.Spouse.Madonna

Madonna Marriage.Spouse 2000

Who did Madonna marry in 2000

lex lex

joinjoin

28


Marriage.Spouse.Madonna Marriage.StartDate



lex lex

joinjoin

bridging

Marriage.(Spouse.Madonna u StartDate.2000)

28


Marriage.Spouse.Madonna Marriage.StartDate



lex lex

joinjoin

bridging

Marriage.(Spouse.Madonna u StartDate.2000)

Later: a more general solution called floating parser

• Wang et al., 2015; Pasupat and Liang, 2015

28

Type raising

Traverses Oregon

Traverse(Oregon)

Traverse

traverses

Oregon

Oregon

29

Type raising

Traverses Oregon

Traverse(Oregon)

Traverse

traverses

Oregon

Oregon

traverses Oregon or traverses Nevada

Traverse(Oregon) t Traverse(Nevada)

Traverse(Oregon)

Traverse

traverses

Oregon

Oregon

or Traverse(Nevada)

Traverse

traverses

Nevada

Nevada

29

Type raising

Traverse(Oregon) t Nevada

Traverse(Oregon)

Traverse

traverses

Oregon

Oregon

or Nevada

Nevada

How to apply the binary on multiple arguments?

30

Solution 1

(ConstFn λx.λy.λb.b(x) t b(y)) Disj ⇒ or

31

Solution 1

(ConstFn λx.λy.λb.b(x) t b(y)) Disj ⇒ or

Traverses Oregon or Nevada or Colorado

Another lexical entry?

31

Type raising

Type raise the entity to a function that is applied on a binary

(ApplyFn λx.λf.f(x)) FuncSet⇒ Set

(ConstFn λa.λb.λg.a(g) t b(g)) Disj ⇒ or

Traverse(Oregon) t Traverse(Nevada)

Traverse

traverses

λg.g(Nevada) t g(Oregon)

λf.f(Oregon)

Oregon

Oregon

λb.λg.g(Nevada) t b(g)

λa.λb.λg.a(g) t b(g)

or

λf.f(Nevada)

Nevada

Nevada

32

Outline



– Example

– Lexicon

– Modeling

– CCG

– Exercise

33

CCG

Standard formalism in semantics

34

CCG


Lexicon:

fun ` ADJ : λx.fun(x)

fun ` N/N : λf.λx.fun(x) ∧ f(x)

34

CCG


Lexicon:

fun ` ADJ : λx.fun(x)

fun ` N/N : λf.λx.fun(x) ∧ f(x)

Handful of combinators (grammar)

A/B : f B : g ⇒ A : f(g) (>)

B : g A\B : f ⇒ A : f(g) (<)

34

CCG

Main difference:

• CCG pushed complexity from grammar to lexicon

• lambda-DCS tries to push it from lexicon to learning

35

CCG

Main difference:



Rationale:

• CCG originates in linguistics

• Lambda-DCS originates in NLP

35

CCG

Main difference:



Rationale:

• CCG originates in linguistics

• Lambda-DCS originates in NLP

• CCG-based semantic parsing addressed many issues with typeraising, factored lexicons, etc. [Zettlemoyer and Collins, 2007;Kwiatkowski et al., 2011]

35

Philosophy: simple grammar and lexicon

• Capturing correct derivations only requires complex rules

36



• Simple rules generate overapproximation of good derivations

36



• Simple rules generate overapproximation of good derivations

Disambiguate at learning time!

36

Outline



– Example

– Lexicon

– Modeling

– CCG

– Exercise

37

Exercise

Write a grammar that parses utterances

You can use class2 demo.lexicon and class2 demo.grammar that are onthe website

They are also at /home/shared/esslli/semparse

You can also start with ConstantFn entries that parse the entire uttearnceand decompose

38

Exercise


Top 5 cities by area

Major cities with at least 140,000 inhabitants

How many states have capitals with at least 200,000 inhabitants

State bordering Oregon and Nevada

Check if the grammar parses the sentence:

States bordering Oregon and Nevada and Arizona

39

Summary

• Grammars build derivations which compositionally provide logicalforms

• Lexicons map phrases to basic logical forms

• Learning lexicons is hard so we prefer to push the complexity tolearning

40

Documents

Executable Semantic Parsing