CLIN-Utrecht-99

1
MC-TAG, flexible composition, etc. ARAVIND K.
JOSHI March 15 2006

2
Feature Structures and Unification
Adjoining as unification
tr br
X
t b
b
a
X
tf bf
X
t È tr
X
g
br
tf
X
b
b È bf
No directionality involved in the composition
3
Feature Structures and Unification
Substitution as unification
tr br
X
a
a1
t
X
g
t È tr
X
br
a1
No directionality involved in the composition
4
Flexible Composition (FC)

• All formal grammars (FG) have some notion of FC
• However, it is not the case that for all FG,
  FC is productive, in the sense that -- FC
  gives to new and useful derivations and/or --
  new word order variations, scope ambiguities,
  for example
• In a CFG, a rule such as A
  B C either B is a function taking C as
  the argument or vice versa, i.e., A
  (A/C) C or A B (B\A) -- same
  derived tree, different derivations,
  but not useful -- same word order

5
Flexible Composition (FC)

• CFG rules as one level trees

a2
a3
S
S
S
a1
NP3 VP3
NP2 S VP2
NP1 S VP1
S
a2
S
a3
S
a1
NP3 VP3
NP2 S VP2
NP1 S VP1

• Same derived tree, two different derivations
• Same word order NP1 NP2 NP3 VP3 VP2 VP1
• Structure adjacency (for one level tree
  structures) does not buy anything more

6
Standard TAG

• Derived Tree
• Derivation tree -- different ways of
  walking over the derivation tree --
  top-down -- bottom-up --
  inside-out -- It does not make any
  difference in terms of the the set of
  strings that can be derived

7
Multi-Component TAG (MC-TAG)

• Different motivations
• Tree-local -- Tree-local MC-TAG weakly
  equivalent to Standard TAG
• Set-local

8
Flexible Composition
Adjoining as Wrapping
a at x
Split
a
X
X
X
a1 supertree of a at X
a2 subtree of a at X
9
Flexible Composition
Adjoining as Wrapping
X
b
a
X
X
a1 supertree of a at X
X
g
b
X
a2 subtree of a at X
a wrapped around b i.e., the two components a1
and a2 are wrapped around b
10
Flexible Composition
Wrapping as substitutions and adjunctions
S
b
a
S
S
NP(wh)
VP
NP
VP
NP
V
S
V
NP
think
substitution
likes
e
- We can also view this composition as a
wrapped around b - Flexible composition
adjoining
11
Flexible Composition
Wrapping as substitutions and adjunctions
a
S
substitution
a1
S
adjoining
b
S
NP(wh)
S
VP
a2
NP
VP
NP
V
S
V
NP
think
likes
e
a1 and a2 are the two components of a a1
attached (adjoined) to the root node S of b a2
attached (substituted) at the foot node S of b

Leads to multi-component TAG (MC-TAG)
12
Multi-component LTAG (MC-LTAG)

a
a1
b
b
a2
The two components are used together in one
composition step. Both components attach to
nodes in b, an elementary tree. This preserves
locality.
13
Tree-Local Multi-component LTAG (MC-LTAG)
- How can the components of MC-LTAG compose
preserving locality of LTAG - Tree-Local MC-LTAG
-- Components of a set compose only with an
elementary tree or an elementary
component- Flexible composition -- The
notion of the derivation tree still holds for
the Tree-Local MC-TAG -- Different
ways of walking over the derivation tree
-- It can make a difference in terms of the
structures that can be derived!
14
Tree-Local MC-LTAG and flexible semantics

• Three clauses, C1, C2, and C3, each clause
  can be either a single elementary tree or a
  multi- component tree set with two components
• The verb in C1 takes the verb in C2 as the
  argument and the verb in C2 takes the verb in
  C3 as the argument
• Flexible composition allows us to compose the
  three clauses in three ways

15
Tree-Local MC-LTAG and flexible semantics
Three ways of composing C1, C2, and C3
(1)
C1 C2 C3
C1 C2 C3
(2)
C1 C2 C3
(3)

• The third mode of composition can give rise
  to new strings, which are not obtainable from
  the first two ways only

16
Scrambling N3 N2 N1 V3 V2 V1
VP
VP
VP
N3 VP
N2 VP
N1 VP
VP
VP
VP
VP
N2
VP
VP
N1
VP
VP
N3
e
e
V2
V1
e
V3
17
Scrambling N3 N2 N1 V3 V2 V1
(flexible composition)
VP
VP
VP
N3 VP
N2 VP
N1 VP
VP
VP
VP
N1
VP
N2
VP
VP
VP
VP
N3
e
e
V2
V1
e
V3
18
Tree-local MC-TAG

• Usually two components only
• One component can be lexically empty (null)
• Components are not independent --
  immediate domination -- domination --
  co-indexing
• Flexible composition has to respect these
  constraints -- some examples
  -- Scrambled NPs --
  Extraposition from NP

19
Extraposition from NP An example
(1) The gardener who the woman kept calling all
day finally came. (1) The gardener
finally came who the woman kept calling all
day. (2) The gardener who the woman who had lost
her keys kept calling all day finally
came. (2) The gardener who the woman kept
calling all day finally came who had lost her
keys.
20
S
NP VP
The gardener finally came
S
S
S
who the woman kept calling all day
NP VP
The gardener finally came
21
S
b11 b12
b1
NP S
NP VP
NP S(i) S S(i)
The gardener finally came
e
who the woman kept calling all day
S
S
S
who the woman kept calling all day
NP VP
The gardener finally came
22
S
b11 b12
b1
NP S
NP VP
NP S(i) S S(i)
The gardener finally came
e
who the woman kept calling all day
S
S
S
who the woman kept calling all day
NP VP
Tree local MC-LTAG for NP Extraposition
The gardener finally came
23
(2) The gardener who the woman who had lost her
keys kept calling all day finally came. (2)
The gardener who the woman kept calling all day
finally came who had lost her keys.

S
S (i)
S
who had lost her keys
NP VP
finally came
NP S
The gardener who the woman (i) kept calling
all day

• Not possible even with flexible composition if
  the constraints between the two components are
  to be respected