Tree Adjoining Grammars

Syntax in LTAG

Laura Kallmeyer & Benjamin Burkhardt

HHU Düsseldorf

WS 2017/2018

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Outline

1 The derivation tree

2 Design principles for elementary trees

3 Sample derivations

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Derivation trees: Example derivation

NP

Adam

VP

VP∗

Adv

always

S

VP

NP↓V

ate

NP↓ NP

NP∗

Det

the

NP

apple

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Derivation trees: Example derivation

S

VP

VP

NP

NP

apple

Det

the

V

ate

Adv

always

NP

Adam

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Derivation trees

TAG derivations are uniquely described by derivation trees. The

derivation tree contains:

nodes for all elementary trees used in the derivation, and

edges for all adjunctions and substitutions performed

throughout the derivation, and

edge labels indicating the target node of the rewriting

operation.

Whenever an elementary tree γ rewrites the node at Gorn address pin the elementary tree γ′, there is an edge from γ′ to γ labeled with p.

Note that derivation trees are unordered trees.

Adjunction edges are sometimes depicted as dashed lines,

substitution edges as solid lines.

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Derivation trees

For the node addresses of elementary trees, Gorn addresses are

used:

the root has address ε (or 0)

the ith daughter of the node with address p has address pi.

0

2

22

221

21

212211

1

1312

121

11

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Derivation trees: example

Derived tree:

S

VP

VP

NP

NP

apple

Det

the

V

ate

Adv

always

NP

Adam

Derivation tree:

ate

adam apple

the

always

1 22

0

2

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Linguistic analyses with LTAG

What is an elementary tree, and what is its shape?

elementary trees?⇐=

syntactic/semantic properties of

linguistic objects

⇒ Syntactic design principles from Frank (2002):

Lexicalization

Fundamental TAG Hypothesis (FTH)

Condition on Elementary Tree Minimality (CETM)

θ-Criterion for TAG

⇒ Semantic design principles [Abeillé & Rambow (2000)]

⇒ Design principle of economy

Further overviews are given in chapter 5 of Lichte (2015) (in

German) and chapter 4 of Kallmeyer (2010).

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Syntactic design principles (1): Lexicalization

Each elementary tree has at least one non-empty lexical item, its

lexical anchor.

⇒ All widely used grammar formalisms support some kind of

lexicalization!

⇒ TAG → LTAG: Lexicalized Tree-Adjoining Grammar

[Schabes & Joshi (1990); Joshi & Schabes (1991)]

Recall: reasons for lexicalization

Formal properties: A �nite lexicalized grammar provides

�nitely many analyses for each string (�nitely ambiguous).

Linguistic properties: Syntactic properties of lexical items

can be accounted for more directly.

Parsing: The search space during parsing can be delimited

(grammar �ltering).

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Syntactic design principles (2): FTH

Fundamental TAG Hypothesis (FTH); [Frank (2002)]

Every syntactic dependency is expressed locally within an

elementary tree.

“syntactic dependency”

valency/subcategorization

binding

�ller-gap constructions

. . .

“expressed within an elementary tree”

terminal leaf (i.e. lexical anchor)

nonterminal leaf (substitution node and footnode)

marking an inner node for obligatory adjunction

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Syntactic design principles (2): FTH

Examples of ill-formed elementary trees:

S

VP

V

persuades

NP↓

S

VP

NP

ε

V

ate

NP↓

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Complex primitives

Joshi (2004):

Complicate locally, simplify globally.

“[...] start with complex (more complicated) primitives, which capturedirectly some crucial linguistic properties and then introduce somegeneral operations for composing these complex structures (primitive orderived). What is the nature of these complex primitives? In theconventional approach the primitive structures (or rules) are kept assimple as possible. This has the consequence that information (e.g.,syntactic and semantic) about a lexical item (word) is distributed overmore than one primitive structure. Therefore, the informationassociated with a lexical item is not captured locally, i.e., within thedomain of a primitive structure.”[Joshi (2004)]

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Syntactic design principles (3): CETM

Condition on Elementary Tree Minimality (CETM); ; [Frank (2002)]

The syntactic heads in an elementary tree and their projections must

form the extended projection of a single lexical head.

Examples of ill-formed elementary trees:

S

VP

VP

V

arrived

AP↓

NP↓

S

VP

S

VP

NP↓V

to eat

NP

ε

NP↓V

persuades

NP↓

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Syntactic design principles (4): θ-Criterion for TAG

Thematic role (θ-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 Agent,

Theme, Patient, Goal, Source, Experiencer etc.

example: Bart kicked the ball.kicked predicate

Bart Agent

ball Theme/Patient

The ball was kicked by Bart.kicked predicate

Bart Agent

ball Theme/Patient

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Syntactic design principles (4): θ-Criterion for TAG

θ-Criterion (TAG version)

a. If H is the lexical head of an elementary tree T, H assigns all of

its θ-roles in T.

b. If A is a frontier non-terminal of elementary tree T, A must be

assigned a θ-role in T.

[Frank (2002)]

=⇒ Valency/subcategorization is expressed only with nonterminal

leaves!

S

VP

V

sleeps

NP↓

S

VP

S∗

V

try

NP↓

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Further design principles

Semantic design principles

Predicate-argument co-occurrence:

Each elementary tree associated with a predicate contains a

non-terminal leaf for each of its arguments.

Semantic anchoring:

Elementary trees are not semantically void (to, that.)

Compositional principle:

An elementary tree corresponds to a single semantic unit.

Design principle of economy

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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Modi�cation and functional elements

How to insert modi�ers (e.g. easily) and functional elements(complementizers, determiners, do-auxiliaries, ...)?

either as co-anchor in the elementary tree of the lexical item

they are associated with

S

S

VP

sleeps

NP↓

Comp

that

S

VP

AP

easily

VP

sleeps

NP↓

or by separate auxiliary trees (e.g., XTAG grammar)

S

S∗

Comp

that

VP

AP

easily

VP∗

⇒ Footnodes/Adjunctions indicate both complementation and

modi�cation.

⇒ Enhancement of the CETM: [see Abeillé & Rambow (2000)]

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Sample derivations: NP and PP complements

(1) Adam gave Eve the apple.

Elementary trees:

S

VP

NP↓NP↓V

gave

NP↓

NP

N

Adam

NP

N

Eve

NP

N

apple

NP

NP∗

Det

the

Derivation tree:gave

adam eve apple

the

1 22 23

0

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Sample derivations: NP and PP complements

(2) Adam gave the apple to Eve.

Elementary trees:

S

VP

PP

NP↓P

to

NP↓V

gave

NP↓

NP

N

Adam

NP

N

Eve

NP

N

apple

NP

NP∗

Det

the

Derivation tree:gave

adam apple eve

the

1 22 232

0

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Sample derivations: Sentential complements

(3) Adam hopes that Eve comes.

Elementary trees:

S

VP

S∗

V

hopes

NP↓

S

VP

V

comes

NP↓

NP

N

Adam

NP

N

Eve

S

S∗

Comp

that

Derivation tree: comes

adam

eve

hopes

that

0 1

0

1

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Sample derivations: long-distance dependency

(4) Whati did Adam say (that) Eve ate _i?

NP

N

what

S

S

VP

S∗

V

say

NP↓

Aux

did

NP

N

Adam

NP

N

Eve

S

S

S

VP

NP

εi

V

ate

NP↓

COMP

ε

NPi↓

Derivation tree: ate

whateve did_say

adam

221 1 2

21

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Sample derivations: Modi�ers

(5) The good student participated in every course during the semester.

Elementary trees:

S

VP

PP

NP↓P

in

V

part.

NP↓

NP

N

student

NP

N

course

NP

N

semester

NP

NP∗

Det

the

NP

NP∗

Det

every

N

N∗

AP

good

VP

PP

NP↓P

during

VP∗

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Sample derivations: Modi�ers

Derivation tree:part_in

stud course during

the good every semester

the

1 222 2

0 1 0 22

0

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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 (CSLI Lecture Notes 107), 1–68. Stanford, CA: CSLI Publications.

Frank, Robert. 2002. Phrase structure composition and syntactic dependencies. Cambridge,

Mass: 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/.

Kallmeyer, Laura. 2010. Parsing beyond context-free grammars Cognitive Technologies.

Heidelberg: Springer.

Lichte, Timm. 2015. Syntax und Valenz. Zur Modellierung kohärenter und elliptischer

Strukturen mit Baumadjunktionsgrammatiken (Empirically Oriented Theoretical

Morphology and Syntax 1). Berlin: Language Science Press.

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/.