Practical SCFGs

Synchronous context-free grammar

S → NP1 VP2 / NP1 VP2

NP → watashi wa / I NP → hako wo / the boxVP → NP1 V2 / V2 NP1

V → akemasu / open

Originally: syntax-directed translation (Lewis & Stearns 1966; Aho and Ullman 1969)

Translation as parsingS

NP VP

NP Vwatashi wa

akemasuhako wo

S

NP VP

V NPI

open the box

watashi wa hako wo akemasu I open the box

Questions about SCFGs

•How do n-gram language models fit in?

•How do we get the grammar?

•Is this really a plausible model of translation?

•Does it actually work? Why or why not?

Parsing as weighted deductionFor sentence w1…wn, grammar G with nonterminals N

[i,X, j] 8i, j 2 0, ..., n,X 2 N

[X ! ZY ] 8X ! XY 2 PG

[X ! w] 8X ! w 2 PG

[wi = w] 8i 2 1, ..., naxioms:

items:inference rules:

[1, S, n]goal:

[X ! w] : u [wi+1 = w] : v

[i,X, i+ 1] : u⌦ v

[X ! Y Z] : u [i, Y, k] : v [k, Z, j] : y

[i,X, j] : u⌦ v ⌦ y

Parsing as weighted deductionFor sentence w1…wn, grammar G with nonterminals N

[i,X, j] 8i, j 2 0, ..., n,X 2 N

[X ! ZY ] 8X ! XY 2 PG

[X ! w] 8X ! w 2 PG

[wi = w] 8i 2 1, ..., naxioms:

items:inference rules:

[1, S, n]goal:

[X ! w] : u [wi+1 = w] : v

[i,X, i+ 1] : u⌦ v

[X ! Y Z] : u [i, Y, k] : v [k, Z, j] : y

[i,X, j] : u⌦ v ⌦ y

From proof to (pseudo)codeInput: w1…wn, grammar Gfor i in 1,…,n: for X->w_i in P(G): chart[i-1,X,i] := u(X->w_i)for l in 2,…,n: for i in 0,…,n-l: j := i+l for k in i+1,…,j-1: for X->YZ in P(G): chart[i,X,j] += ( chart[i,Y,k] * chart[k,Z,j] * u(X->YZ))return chart[0,S,n]

From proof to (pseudo)codeInput: w1…wn, grammar Gfor i in 1,…,n: for X->w_i in P(G): chart[i-1,X,i] := u(X->w_i)for l in 2,…,n: for i in 0,…,n-l: j := i+l for k in i+1,…,j-1: for X->YZ in P(G): chart[i,X,j] += ( chart[i,Y,k] * chart[k,Z,j] * u(X->YZ))return chart[0,S,n]

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

I saw her duck

NP

VP

PRP VBD PRP$ NN

S

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

I saw her duck

NP

VP

PRP VBD PRP$ NN

SNP

VP

PRP VBD PRP$ NN

S

yo vi su pato

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

I saw her duck

SBAR

VP

PRP VBD PRP VB

SSBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

I saw her duck

SBAR

VP

PRP VBD PRP VB

SSBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

Parsing

I1 saw2 her3 duck4

PRP0,1

VBD1,2

VP1,4

PRP$2,3 NN3,4

NP2,4

PRP2,3 VB3,4

SBAR2,4

S0,4

I saw her duck

SBAR

VP

PRP VBD PRP VB

SSBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

VP

PRP

SBAR

VBD

PRP VB

VP

PRPSBAR

VBD

VBPRP

score(e, a|f) = ✓ · h(e, a, f)

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

S

VP

PRP

SBAR

VBD

PRP VB

VP

PRPSBAR

VBD

VBPRP

SCFG feature decomposes over structure!

PRP VBD PRP VB

yo vi ella agacharse

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

VP

PRP

SBAR

VBD

PRP VB

VP

PRPSBAR

VBD

VBPRP

Bigram language model feature does not!p(e) =

JY

j=1

p(ej |ej�1)

$^

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

$^

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

$^

bigramhere

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

$^

bigramhere

only evaluated

here

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

$^

bigramhere

only evaluated

here

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

$^

bigramhere

only evaluated

here

Parsing

I saw her duck

SBAR

VP

PRP VBD PRP VB

S

SBAR

VP

PRP VBD PRP VB

S

yo vi ella agacharse

score(e, a|f) = ✓ · h(e, a, f)

$^

bigramhere

only evaluated

here

Decoding as weighted deductionFor sentence w1…wn, grammar G with nonterminals N

[i,X, j] 8i, j 2 0, ..., n,X 2 N

[X ! ZY ] 8X ! XY 2 PG

[X ! w] 8X ! w 2 PG

[wi = w] 8i 2 1, ..., naxioms:

items:inference rules:

[1, S, n]goal:

[X ! w] : u [wi+1 = w] : v

[i,X, i+ 1] : u⌦ v

[X ! Y Z] : u [i, Y, k] : v [k, Z, j] : y

[i,X, j] : u⌦ v ⌦ y

Decoding as weighted deductionFor sentence w1…wn, grammar G with nonterminals N

[X ! ZY ] 8X ! XY 2 PG

[wi = w] 8i 2 1, ..., naxioms:

items:inference rules:

goal:

[X ! w/w0] 8X ! w/w0 2 PG

[w1, i,X, j, w2] 8i, j 2 0, ..., n,X 2 N

[X ! w/w0] : u [wi+1] = w] : v

[w0, i,X, i+ 1, w0] : u⌦ v

[X ! Y Z] : u [w1, i, Y, k, w2] : v [w3, k, Z, j, w4] : y

[w1, i,X, j, w4] : u⌦ v ⌦ y ⌦ ↵(w2w3)

[̂ , 1, S, n, $]

Decoding as weighted deductionFor sentence w1…wn, grammar G with nonterminals N

[X ! ZY ] 8X ! XY 2 PG

[wi = w] 8i 2 1, ..., naxioms:

items:inference rules:

goal:

[X ! w/w0] 8X ! w/w0 2 PG

[w1, i,X, j, w2] 8i, j 2 0, ..., n,X 2 N

[X ! w/w0] : u [wi+1] = w] : v

[w0, i,X, i+ 1, w0] : u⌦ v

[X ! Y Z] : u [w1, i, Y, k, w2] : v [w3, k, Z, j, w4] : y

[w1, i,X, j, w4] : u⌦ v ⌦ y ⌦ ↵(w2w3)

[̂ , 1, S, n, $]

Decoding as weighted deductionFor sentence w1…wn, grammar G with nonterminals N

[X ! ZY ] 8X ! XY 2 PG

[wi = w] 8i 2 1, ..., naxioms:

items:inference rules:

goal:

[X ! w/w0] 8X ! w/w0 2 PG

[w1, i,X, j, w2] 8i, j 2 0, ..., n,X 2 N

[X ! w/w0] : u [wi+1] = w] : v

[w0, i,X, i+ 1, w0] : u⌦ v

[X ! Y Z] : u [w1, i, Y, k, w2] : v [w3, k, Z, j, w4] : y

[w1, i,X, j, w4] : u⌦ v ⌦ y ⌦ ↵(w2w3)

[̂ , 1, S, n, $]

Decoding as weighted deduction

inference rules:

goal:

[X ! w/w0] : u [wi+1] = w] : v

[w0, i,X, i+ 1, w0] : u⌦ v

[X ! Y Z] : u [w1, i, Y, k, w2] : v [w3, k, Z, j, w4] : y

[w1, i,X, j, w4] : u⌦ v ⌦ y ⌦ ↵(w2w3)

[̂ , 1, S, n, $]

What is the complexity of this algorithm?

Decoding as weighted deduction

inference rules:

goal:

[X ! w/w0] : u [wi+1] = w] : v

[w0, i,X, i+ 1, w0] : u⌦ v

[X ! Y Z] : u [w1, i, Y, k, w2] : v [w3, k, Z, j, w4] : y

[w1, i,X, j, w4] : u⌦ v ⌦ y ⌦ ↵(w2w3)

[̂ , 1, S, n, $]

What is the complexity of this algorithm?

O(N3I3⌃2(n�1))

exponential in n-gram order

Huang and Chiang Forest Rescoring

Cube Pruning

12

(VP held ⋆ meeting3,6 )

(VP held ⋆ talk3,6 )

(VP hold ⋆ conference3,6 )

(PPwith

⋆Sh

aron

1,3

)

(PPalon

g⋆Sh

aron

1,3

)

(PPwith

⋆Sh

alon

g

1,3

)

PP1, 3 VP3, 6

VP1, 6

monotonic grid?1.0 3.0 8.0

1.0 2.0 4.0 9.0

1.1 2.1 4.1 9.1

3.5 4.5 6.5 11.5

Huang and Chiang Forest Rescoring

Cube Pruning

13

(VP held ⋆ meeting3,6 )

(VP held ⋆ talk3,6 )

(VP hold ⋆ conference3,6 )

(PPwith

⋆Sh

aron

1,3

)

(PPalon

g⋆Sh

aron

1,3

)

(PPwith

⋆Sh

alon

g

1,3

)

PP1, 3 VP3, 6

VP1, 6

non-monotonic grid due to LM combo costs 1.0 3.0 8.0

1.0 2.0 + 0.5 4.0 + 5.0 9.0 + 0.5

1.1 2.1 + 0.3 4.1 + 5.4 9.1 + 0.3

3.5 4.5 + 0.6 6.5 +10.5 11.5 + 0.6

Huang and Chiang Forest Rescoring

Cube Pruning

13

(VP held ⋆ meeting3,6 )

(VP held ⋆ talk3,6 )

(VP hold ⋆ conference3,6 )

(PPwith

⋆Sh

aron

1,3

)

(PPalon

g⋆Sh

aron

1,3

)

(PPwith

⋆Sh

alon

g

1,3

)

PP1, 3 VP3, 6

VP1, 6

non-monotonic grid due to LM combo costs 1.0 3.0 8.0

1.0 2.0 + 0.5 4.0 + 5.0 9.0 + 0.5

1.1 2.1 + 0.3 4.1 + 5.4 9.1 + 0.3

3.5 4.5 + 0.6 6.5 +10.5 11.5 + 0.6

bigram (meeting, with)

Huang and Chiang Forest Rescoring

Cube Pruning

14

1.0 3.0 8.0

1.0 2.5 9.0 9.5

1.1 2.4 9.5 9.4

3.5 5.1 17.0 12.1

(VP held ⋆ meeting3,6 )

(VP held ⋆ talk3,6 )

(VP hold ⋆ conference3,6 )

(PPwith

⋆Sh

aron

1,3

)

(PPalon

g⋆Sh

aron

1,3

)

(PPwith

⋆Sh

alon

g

1,3

)

PP1, 3 VP3, 6

VP1, 6

non-monotonic grid due to LM combo costs

Huang and Chiang Forest Rescoring

Cube Pruning

15

1.0 3.0 8.0

1.0 2.5 9.0 9.5

1.1 2.4 9.5 9.4

3.5 5.1 17.0 12.1

(VP held ⋆ meeting3,6 )

(VP held ⋆ talk3,6 )

(VP hold ⋆ conference3,6 )

(PPwith

⋆Sh

aron

1,3

)

(PPalon

g⋆Sh

aron

1,3

)

(PPwith

⋆Sh

alon

g

1,3

)k-best parsing

(Huang and Chiang, 2005)

• a priority queue of candidates

• extract the best candidate

Huang and Chiang Forest Rescoring

Cube Pruning

16

(VP held ⋆ meeting3,6 )

(VP held ⋆ talk3,6 )

(VP hold ⋆ conference3,6 )

(PPwith

⋆Sh

aron

1,3

)

(PPalon

g⋆Sh

aron

1,3

)

(PPwith

⋆Sh

alon

g

1,3

)

• a priority queue of candidates

• extract the best candidate

• push the two successors

1.0 3.0 8.0

1.0 2.5 9.0 9.5

1.1 2.4 9.5 9.4

3.5 5.1 17.0 12.1

k-best parsing (Huang and Chiang, 2005)

Huang and Chiang Forest Rescoring

Cube Pruning

17

(VP held ⋆ meeting3,6 )

(VP held ⋆ talk3,6 )

(VP hold ⋆ conference3,6 )

(PPwith

⋆Sh

aron

1,3

)

(PPalon

g⋆Sh

aron

1,3

)

(PPwith

⋆Sh

alon

g

1,3

)

1.0 3.0 8.0

1.0 2.5 9.0 9.5

1.1 2.4 9.5 9.4

3.5 5.1 17.0 12.1

• a priority queue of candidates

• extract the best candidate

• push the two successors

k-best parsing (Huang and Chiang, 2005)

Cube pruning

•Parse as usual using CKY.

•Revisit chart in topological order expanding language model.

•Only produce top k expansions per cell.

•Many variants (lazy, A*, etc.)

ParsingNN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR

Parsing

I1 saw2 her3 duck4

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

PRP2,3

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

PRP2,3

NN3,4

VB3,4

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

PRP2,3

NN3,4

VB3,4

NP2,4

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

PRP2,3

NN3,4

VB3,4

NP2,4 SBAR2,4

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

PRP2,3

NN3,4

VB3,4

NP2,4 SBAR2,4

VP1,4

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

PRP2,3

NN3,4

VB3,4

NP2,4 SBAR2,4

VP1,4

Parsing

I1 saw2 her3 duck4

PRP0,1

NN → duck

PRP → I

VBD → saw

PRP$ → her

NP → PRP$ NN

VP → VBD NP

S → PRP VP

PRP → her

VB → duckSBAR → PRP VB

VP → VBD SBAR VBD1,2

PRP$2,3

PRP2,3

NN3,4

VB3,4

NP2,4 SBAR2,4

VP1,4

S0,4

Japanese watashi wa

hako wo hako wo akemasu akemasu

hako wo akemasu

English I

the box box open

open the open the box

p(E|J) 1.0 0.5 0.5 0.5 0.5 1.0

A translation model is simply a probabilistic phrase dictionary.

Japanese watashi wa

hako wo hako wo akemasu akemasu

hako wo akemasu

English I

the box box open

open the open the box

p(E|J) 1.0 0.5 0.5 0.5 0.5 1.0

Japanese watashi wa

hako wo hako wo akemasu akemasu

hako wo akemasu X1 X2 akemasu

akemasu X1 watashi wa X1 X2

X1 hako wo X2

English I

the box box open

open the open the box X1 open X2

open X1 I X2 X1

X1 X2 the box

p(E|J) 1.0 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0

Phrase ExtractionI open the box

watashiwa hako woakemasu

Phrase ExtractionI open the box

watashiwa hako woakemasu

word alignment: expectation maximization

Phrase ExtractionI open the box

watashi

wa

hako

wo

akemasu

Phrase ExtractionI open the box

watashi

wa

hako

wo

akemasu

akemasu / open

Phrase ExtractionI open the box

watashi

wa

hako

wo

akemasu

watashi wa / I

Phrase ExtractionI open the box

watashi

wa

hako

wo

akemasu

hako wo / the box

Phrase ExtractionI open the box

watashi

wa

hako

wo

akemasu

✘hako wo / open the box

Phrase ExtractionI open the box

watashi

wa

hako

wo

akemasu

hako wo akemasu / open the box

Phrase ExtractionI open the box

watashi

wa

hako

wo

_ akemasu / open _

Phrase ExtractionI open the box

watashi

wa

hako

wo

_1 _2 akemasu/ _1 open _2

Phrase ExtractionI open the box

watashi

wa

hako

wo

watashi wa hako wo _ / I _ the box

Extrac0ng,Syntac0c,Rules

澳洲是 与 北 � 有 邦

交的 少数国家之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

NNP

PP

NP

NP

NP

NPPPNPCOMP

VP

Extrac0ng,Syntac0c,Rules

澳洲是 与 北 � 有 邦

交的 少数国家之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

VP

SNP

NP

NNP

PP

NP

NP

NP

NPPPNPCOMP

VP

Extrac0ng,Syntac0c,Rules

澳洲

是 与 北 � 有 邦交

的 少数

国家

之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

VP → 与 北 � 有 邦交, have diplomatic relations with North Korea

VP

SNP

NP

NNP

PP

NP

NP

NP

NPPPNPCOMP

VP

Extrac0ng,Syntac0c,Rules

澳洲

是 与 北 � 有 邦交

的 少数

国家

之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

VP → 与 北 � 有 邦交, have diplomatic relations with North Korea

NP → 与 北 � 有 邦交 的 少数 国家, the few countries that have diplomatic relations with North Korea

VP

SNP

NP

NP → VP 的 少数 国家, the few countries that VP

NNP

PP

NP

NP

NP

NPPPNPCOMP

VP

Extrac0ng,Syntac0c,Rules

澳洲

是 与 北 � 有 邦交

的 少数

国家

之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

VP → 与 北 � 有 邦交, have diplomatic relations with North Korea

NP → 与 北 � 有 邦交 的 少数 国家, the few countries that have diplomatic relations with North Korea

VP

SNP

NP

NP → VP 的 少数 国家, the few countries that VP

NP → VP 的 NP, the NP that VP

NNP

PP

NP

NP

NP

NPPPNPCOMP

VP

Extrac0ng,Syntac0c,Rules

澳洲

是 与 北 � 有 邦交

的 少数

国家

之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

VP → 与 北 � 有 邦交, have diplomatic relations with North Korea

NP → 与 北 � 有 邦交 的 少数 国家, the few countries that have diplomatic relations with North Korea

VP

SNP

NP

NNP

PP

NP

NP

NP

NPPPNPCOMP

VP

Extrac0ng,Syntac0c,Rules

澳洲

是 与 北 � 有 邦交

的 少数

国家

之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

VP → 与 北 � 有 邦交, have diplomatic relations with North Korea

??? → 的 少数 国家, !the few countries that

NP → 与 北 � 有 邦交 的 少数 国家, the few countries that have diplomatic relations with North Korea

VP

SNP

NP

NNP

PP

NP

NP

NP

NPPPNPCOMP

VP

Extrac0ng,Syntac0c,Rules

澳洲

是 与 北 � 有 邦交

的 少数

国家

之一

Australia

is

one

of

the

few

countries

that

have

diplomatic

relations

with

North

Korea

VP → 与 北 � 有 邦交, have diplomatic relations with North Korea

??? → 的 少数 国家, !the few countries that

NP → 与 北 � 有 邦交 的 少数 国家, the few countries that have diplomatic relations with North Korea

??? → 澳洲 是, !Australia is

VP

SNP

NP

(Fox, 2002)