The ideal grammar formalism
linguistically adequate:
Working with Tree-Adjoining Grammar
Phenomena:
linearization, agreement, discontinuity, ellipsis, coordination (RNR), . . .
Generalization:
valency, active/passive diathesis, sentence types, alternations, syntaxsemantics interface, syntax-discourse interface
intuitive implementation
Day 2: Linguistic applications using LTAG
Kata Balogh & Timm Lichte
University of Düsseldorf, Germany
computationally adequate:
explicit/formalized
decidable, maybe even tractable
bidirectional
ESSLLI 2015, Barcelona
psycholinguistically adequate:
strictly incremental derivations
correct predictions wrt. processing complexity
SFB 991
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Outline
Example derivation
1
The derivation tree
2
Design principles for elementary trees
Sample derivations in LTAG
3
S
VP
Adv
Pim
always
Feature based TAG
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VP
NP#
NP
NP & PP complements
sentential complements
modifiers
4
2
VP⇤
NP
Det
V
NP#
NP⇤
NP
way
the
finds
3
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4
Example derivation
Derivation trees
TAG derivations are uniquely described by derivation trees. The derivation
tree contains:
S
nodes for all elementary trees used in the derivation, and
edges for all adjunctions and substitutions performed throughout the
derivation, and
VP
NP
Pim
always
edge labels indicating the target node of the rewriting operation.
VP
Adv
Whenever an elementary tree rewrites the node at Gorn address p in the
elementary tree 0, there is an edge from 0 to labeled with p.
NP
V
finds Det
For the node addresses of elementary trees, Gorn addresses are used:
NP
0
the root has address (or 0)
the way
the ith daughter of the node with address p
has address pi.
11
12
121
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Derivation trees: example
What is an elementary tree, and what is its shape?
VP
Adv
always
V
NP
finds Det
way
syntactic/semantic properties of
linguistic objects
) Syntactic design principles from Frank (2002):
Lexicalization
Fundamental TAG Hypothesis (FTH)
Condition on Elementary Tree Minimality (CETM)
-Criterion for TAG
finds
22
?
(=
NP
the way
2
always
) Semantic design principles [Abeillé & Rambow (2000)]
0
) Design principle of economy
the
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211 212 221
5
elementary trees
1
22
VP
Pim
pim
21
Linguistic analyses with LTAG
NP
Derivation tree:
13
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S
Derived tree:
2
1
6
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Syntactic design principles (1): Lexicalization
Syntactic design principles (2): FTH
Each elementary tree has at least one non-empty lexical item, its lexical
anchor.
Fundamental TAG Hypothesis (FTH); [Frank (2002)]
Every syntactic dependency is expressed locally within an elementary tree.
) All widely used grammar formalisms support some kind of lexicalization!
) TAG ! LTAG: Lexicalized Tree-Adjoining Grammar
“syntactic dependency”
valency/subcategorization
binding
filler-gap constructions
...
[Schabes & Joshi (1990); Joshi & Schabes (1991)]
Recall: reasons for lexicalization
Formal properties: A finite lexicalized grammar provides finitely
many analyses for each string (finitely ambiguous).
“expressed within an elementary tree”
Linguistic properties: Syntactic properties of lexical items can be
accounted for more directly.
terminal leaf (i.e. lexical anchor)
nonterminal leaf (substitution node and footnode)
marking an inner node for obligatory adjunction
Parsing: The search space during parsing can be delimited (grammar
filtering).
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Complex primitives
9
Syntactic design principles (3): CETM
Condition on Elementary Tree Minimality (CETM); ; [Frank (2002)]
Joshi (2004):
Complicate locally, simplify globally.
The syntactic heads in an elementary tree and their projections must form
the extended projection of a single lexical head.
“[...] start with complex (more complicated) primitives, which capture directly
some crucial linguistic properties and then introduce some general operations for
composing these complex structures (primitive or derived). What is the nature of
these complex primitives? In the conventional approach the primitive structures
(or rules) are kept as simple as possible. This has the consequence that
information (e.g., syntactic and semantic) about a lexical item (word) is
distributed over more than one primitive structure. Therefore, the information
associated with a lexical item is not captured locally, i.e., within the domain of a
primitive structure.”
[Joshi (2004)]
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Note: We only use simple, non-extended projections!
S|VP
XP
X
head
...
...
VP
...
V
...
... sleeps ...
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11
Syntactic design principles (4): -Criterion for TAG
Syntactic design principles (4): -Criterion for TAG
-Criterion (TAG version)
a. If H is the lexical head of an elementary tree T, H assigns all of its roles in T.
Thematic role ( -role)
the semantic relationship of an argument with its predicate is expressed
through the assignment of a role by the predicate to the argument. Di�erent theta-roles have di�erent labels, such as A����, T����, P������, G���,
S�����, E���������� etc.
b. If A is a frontier non-terminal of elementary tree T, A must be assigned
a -role in T.
[Frank (2002)]
=) Valency/subcategorization is expressed only with nonterminal leaves!
example: Bart kicked the ball.
kicked { predicate
Bart { A����
ball { T����/P������
S
VP
NP#
The ball was kicked by Bart.
kicked { predicate
Bart { A����
ball { T����/P������
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S
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VP
NP#
V
V
sleeps
try
S⇤
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Further design principles
Modification and functional elements
Semantic design principles
How to insert modifiers (e.g. easily) and functional elements (complementizers, determiners, do-auxiliaries, ...)?
Predicate-argument co-occurrence:
Each elementary tree associated with a predicate contains a non-terminal
leaf for each of its arguments.
either as co-anchor in the elementary tree of the lexical item they are
associated with
S
Semantic anchoring:
that
Compositional principle:
NP#
VP
NP#
VP
VP
sleeps
An elementary tree corresponds to a single semantic unit.
AP
sleeps easily
or by separate auxiliary trees (e.g., XTAG grammar)
Design principle of economy
S
The elementary trees are shaped in such a way, that the size of the elementary trees and the size of the grammar is minimal.
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S
Comp
Elementary trees are not semantically void (to, that.)
S
14
Comp S⇤
that
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VP
VP⇤
AP
easily
) Footnodes/Adjunctions indicate both
complementation and modification.
) Enhancement of the CETM: [see
Abeillé & Rambow (2000)]
15
Sample derivations: NP and PP complements
Sample derivations: NP and PP complements
(1) Pim gave Bill a book.
(2) Pim gave a book to Bill.
Elementary trees:
Elementary trees:
S
NP
NP
NP
N
N
N
Det NP⇤
Pim
Bill
book
VP
NP#
NP# NP#
V
S
NP
gave
Derivation tree:
pim
NP
NP
N
N
N
Det NP⇤
Pim
Bill
book
a
P NP#
to
gave
1
PP
NP#
V
gave
NP
VP
NP#
a
NP
22
Derivation tree:
23
bill
book
gave
1
22
pim
0
232
book bill
0
a
a
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Sample derivations: Sentential complements
Sample derivations: long-distance dependency
(3) Pim hopes that Bill wins.
(4) Whati did Pim say (that) Bart read _i ?
Elementary trees:
NP
S
S
VP
NP#
V
NP#
S⇤
NP
S
NP
VP
N
N
Comp
V
Pim
Bill
that
S⇤
N
Aux
what
did
S
V
that
NP
N
N
S⇤
Derivation tree:
1
S
S
NPi #
S
COMP
VP
NP#
say
wins
0
NP
Pim Bart
VP
NP#
wins
hopes
Derivation tree:
V
NP
read
i
read
bill
221
0
bart
hopes
1
2
what did_say
21
1
pim
pim
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S
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19
Sample derivations: Modifiers
Sample derivations: Modifiers
(5) The good student participated in every course during the semester.
Derivation tree:
part_in
Elementary trees:
S
NP
NP
NP
NP
N
N
N
Det NP⇤
NP
1
VP
N
course
stud
VP
NP#
PP
V
stud. course sem. the
Det
NP⇤
every
part. P NP#
AP
N⇤ VP⇤
PP
good
P
1
0
NP#
the
222
good
2
during
0
every
22
semester
0
during
the
in
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20
Feature structures
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21
Features structures
Idea: Instead of atomic categorial symbols, feature structures are used as
non-terminal nodes.
a list of features (e.g. ����) and values (e.g. nom)
feature structures are o�en represented as a�ribute value matrices
(AVM)
Two reasons:
generalizing agreement and case marking (via underspecification)
modelling adjunction constraints (TAG specific)
) smaller grammars that are easier to maintain
sings:
26���
66
66�����
66
66���
64
case assignment:
Joe saw her. / *Joe saw she.
Joe expected her to come. (ECM) / *Joe expected she to come.
person/number agreement:
37
V
77
finite
7
26
37777
���
sg
66
77
64���� 3 775775
feature values:
You sing. / *You sings.
She sings. / *She sing.
This woman sings. / *This woman sing.
These women sing. / *These women sings.
atomic (e.g. for �����)
feature structures (e.g. for ���)
combining constituents ) unify their feature structures
also: definiteness agreement (Hungarian), ...
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Unification
Unification: definition
unification is a (partial) operation on feature structures
intuitively: the operation of combining two feature structures such that
the new feature structure contains all the information of the original
two, and nothing more
e.g.
26
66 ���
66 ���
4
vp
f
���
37
g77 t
pl 77
5
26
66���
66 ���
4
37
g77 =
3 77
5
vp
f
����
partial operation ) unification can fail
e.g.
26
3 2
3
66��� np777 t 666��� np777 = FAIL
64��� sg 75 64��� pl 75
underspecified feature values
e.g.
26
37
66��� np
7t
64���� nom | acc775
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26
3
66��� np 777 =
64���� acc75
26
66���
66
66 ���
64
vp
26
66 ���
64 ����
37
7
3777
pl77
7
3 7777
55
The unification of two feature structures F and G is (if it exists) the smallest
feature structure that is subsumed by both F and G.
That is, (if it exists) F t G is the feature structure with the following three
properties:
(1) F v (F t G)
(2) G v (F t G)
(3) If H is a feature structure such that F v H and G v H, then (F t G) v H.
If there is no smallest feature structure that is subsumed by both F and
G, then we say that F t G is undefined.
Subsumption (F1 v F2 )
26
3
66��� np 777
64���� acc75
A feature structure F1 subsumes (v) another feature structure F2 , i� all the
information that is contained in F1 is also contained in F2 .
24
Reentrancies
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25
Unification: examples
the paths that both lead to the same node ) to the same value
) hence, they share that value
f
g
26
37 "

f
g#
66��� ��� sg
77

����
3
t
����
���
=
f
g
66
7
64���� ��� ��� sg 775
this property of sharing value(s) is called reentrancy
in AVMs: expressed by coindexing the shared values (boxed numbers)
within feature structures:
26
3
26
3

f
g
17
1 val1 7
66����1
77
66����1
77
����1 1 ����2 1
64����2 1 75
64����2 1
75
f
g3 "
26
#

66��� f1 ��� g sg 777 t ���� ��� f���� 3g =
66���� ��� 1
77
4
5
FTAG uses acyclic reentrancies!
between feature structures (in a tree):
f
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Unification (F t G)
����1
1
g f
����1
1
26
66���
66
66����
66
4
for any feature structure F : F t [ ] = [ ] t F = F
f
g
37
77
26
26
373777
66��� 6��� sg7777
66���� 3 77777
66
4
57575
4
��� sg
26
2
33
66��� 1 66��� sg77777
66���� 3 777
66
f 4
g 577
66
77
1
���
����
64
5
the empty feature structure is the identity element for unification
g
26
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27
TAG with feature structures
FTAG
idea: feature structures as non-terminal nodes
at substitution/adjunction the feature structures of the participating
nodes are unified
f
g
26
66���
66
66���
66
66����
4
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���
37
np
7
26
3777
���
sg
66
777
64���� 3 77577
77
nom
75
26
3
66��� np 777
1
66���
7#
66���� nom777
4
5
she
26
66���
66
66���
66
66����
4
f
np
26
���
1 66
64����
nom
she
��� s
37
7
3777
sg77
7
3 77577
77
75
g
26
66���
66
66���
64
Feature-structure based TAG
Vijay-Shanker and Joshi (1988): Feature Structures Based Tree Adjoining
Grammars
s
26
66���
66
66���
64
vp
26
���
1 66
64����
sings
37
7
37
sg7777
7
3 77577
5
annotate each node with two feature structures
split the feature structures ! for adjunction
top features: the relation of the node to the tree above it
bo�om features: the relation of the node to the tree below it
FTAG description of node
1. The relation of to its supertree is called features structure t .
37
vp
7
26
3777
���
sg
777
1 66
64���� 3 77577
5
sings
2. The relation of to its descendants is called features structure b .
at the final derived tree top and bo�om features are unified for all
nodes
28
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FTAG: Substitution
FTAG: Adjunction
Substitution in FTAG
The top features of the root of the tree to substitute unify with the top
features of the substitution node.
Adjunction in FTAG
The top features of the root of the auxiliary tree unify with the top features
of the adjunction node, and the bo�om features of the footnode of the
auxiliary tree unify with the bo�om features of the adjunction node.
X
[t ]
Y[b]1
[t ]t[t2 ]
X
Y#[t2 ]
Y[b]1
...
X
...
[t ]
Y[br ]
X
)
...
substitution nodes (Y#) have only top features
[t ]
Y[by ]
y
[t ]
Y⇤ [bf ]
f
[t ]t[tr ]
Y[by ]
...
r
r
[t ]
y ]t[bf ]
Y[bf
Z
Z
)
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31
FTAG Example: She is singing.
Adjunction constraints
S
modeling adjunction constraints
26
66���
64���
SA: top and bo�om are unifiable
f
g
CAT vp
f
g
CAT vp
OA + SA: feature mismatch between top and bo�om
26
3
vp 77
66CAT
64MODE ind775
26
3
vp 77
66CAT
64MODE ger775
37
37777
3 77
sg7777
577
75
26���
vp
66
26
66
����
1 66
66���
���
6
66
4
64���� ind
f g
V
she
is
2
is
26���
66
66
66���
66
64����
f
g
��� vp
26
3
vp 77 *
66���
64���� ger775
np
26
66���
64����
nom
she
37
37777
sg77
3 7777
577
75
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33
at the final derived tree (a�er all substitutions/adjunctions) the top and
bo�om feature of each node unify:
derivation tree:
1
g
Example (2) She is singing.
S
singing
is
f
top feature of the root node of is unifies with the top feature of the VP
node of singing
bo�om feature of the footnode of is unifies with the bo�om feature of
the VP node of singing
top feature of she unifies with the top feature of the NP node of singing
FTAG Example: She is singing.
she
V
37
vp
77
ind
7
26
3777
����
3
66
777
64��� sg77577
5
feature mismatch at the VP node ) adjunction at VP is obligatory
at adjunction of is & substitution of she:
32
np
26
66����
64���
nom
vp 37
7
1 77
7
ind75
3
vp 77
ger77
5
singing
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3
np77
7
1 7
5
1
V
NA: top and bo�om are unifiable, but there is no auxiliary tree in the
grammar that can be unified with them
26
66���
64���
26���
66
66
66���
66
64����
3
np77
77#
5
26���
66
66���
64����
26
66���
64����
26���
66
66����
66
66���
64
f g
37
37777
3 77
sg7777
577
75
f
S
26���
66
66
66���
66
64����
g
��� vp
26
3
vp 77
66���
64���� ger775
np
26
����
1 66
64���
nom
she
37
37777
3 77
sg7777
577
75
26���
vp
66
26
66
����
1 66
66���
���
6
66
4
64���� ind
V
V
is
singing
37
37777
3 77
sg7777
577
75
26
3
vp 77
66���
64���� ger775
V
singing
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35
Case assignment
Summary & outlook
nouns carry the case, which is ‘checked’
noun case is checked against the case value assigned by the verb during the unification
features of case-assignment:
Summary
derivation tree vs. derived tree
design principles: syntactic / semantic / economy
example derivations: the base cases
hcasei with values: nom | acc | gen | none
) Ns, NPs
hassign-casei with values: nom | acc | none
) case assigners (prepositions, verbs) and S, VP, PP nodes that dominate them
f
g
26���
66
66
66���
66
64����
np
26
66���
64����
nom
she
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37
37777
sg77
3 7777
577
75
f
g
26���
66
66
66���
66
64����
TAG + features structures
S
37
np
26
37777
66��� sg7777
64���� 3 7577
77
acc
5
her
26
3
66��� np 777#
64���� nom75
Tomorrow
Linguistic applications using LTAG (2.)
26
3
vp 77
66���
64����������� nom775
26
3
vp 77
66���
64����� past775
the XTAG grammar
example analyses (extraction)
the syntax-semantics interface
laughed
36
References
Abeillé, Anne & Owen Rambow. 2000. Tree adjoining grammar: An overview. In Anne Abeillé & Owen
Rambow (eds.), Tree adjoining grammars: Formalisms, linguistic analyses and processing, vol. 107 CSLI
Lecture Notes, 1–68. Stanford: CSLI Publications.
Frank, Robert. 2002. Phrase structure composition and syntactic dependencies. Cambridge,MA: MIT Press.
Joshi, Aravind K. 2004. Starting with complex primitives pays o�: complicate locally, simplify globally.
Cognitive Science 28. 637–668.
Joshi, Aravind K. & Yves Schabes. 1991. Tree-Adjoining Grammars and lexicalized grammars. Tech. Rep.
MS-CIS-91-22 Department of Computer and Information Science, University of Pennsylvania.
http://repository.upenn.edu/cis_reports/445/.
Schabes, Yves & Aravind K. Joshi. 1990. Parsing with lexicalized tree adjoining grammar. Tech. Rep.
MS-CIS-90-11 Department of Computer and Information Science, University of Pennsylvania.
http://repository.upenn.edu/cis_reports/542/.
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