Tree-Adjoining Grammars (TAGs)

Seminar Presentation

Grammars for Trees and Graphs

Guadalupe RomeroSourav Dutta

08 November 2018

AGENDA

● TAG

– Definition, types of trees, properties, constraints

– Derivation trees

● Lexicalized Grammars

● Linguistic Relevance of TAG

● Applications of TAG

● Some Variants of TAG

● Conclusion

TREE?

0

Source: Wikipedia

DEFINITION

● a quintuple (Σ, NT, I, A, S)Σ, NT, I, A, S)NT, NT, I, A, S)I, NT, I, A, S)A, NT, I, A, S)S)

– Σ = a finite set of terminal symbols

– NT = a finite set of non-terminal symbols (Σ ∩ NT = ϕ)Σ ∩ NT = ϕ))

– I = a finite set of finite trees (Σ ∩ NT = ϕ)Initial trees)

– A = a finite set of finite trees (Σ ∩ NT = ϕ)Auxiliary trees)

– S = a distinguished non-terminal symbol (Σ ∩ NT = ϕ)S NT)∈ NT)

● Operations

– Substitution

– Adjunction

Types of Trees in TAGs

Elementary Trees Derived Trees

Initial Trees Auxiliary Trees

Source: TAG (Joshi & Shabes 1997)

Types of Trees in TAGs

Source: TAG (Joshi & Shabes 1997)

SUBSTITUTION

● Takes place on a non-terminal leaf node

● The node where substitution is allowed is marked with a ↓

● That node is replaced by a tree with the same node as its root

Source: TAG (Joshi & Shabes 1997)

SUBSTITUTION

Source: TAG (Joshi & Shabes 1997)

ADJUNCTION

● Builds a new tree from an auxiliary tree β (with root X) and any other tree α

● β has a frontier node marked with the symbol *

● A sub-tree t (root X) of α is removed leaving behind a copy of X

● β is copied to the X left behind in α

● Sub-tree t is attached to a foot-node (with label X) of β

Source: TAG (Joshi & Shabes 1997)

ADJUNCTION

1

2

Source: TAG (Joshi & Shabes 1997)

ADJOINING CONSTRAINTS

● Selective Adjunction – S A (Σ ∩ NT = ϕ)T)

– Only members of T A ⊆ A of auxiliary trees

– Adjunction is not mandatory

● Null Adjunction – N A

– No adjunction is allowed

– N A = S A (Σ ∩ NT = ϕ)ϕ))

● Obligatory Adjunction – O A (Σ ∩ NT = ϕ)T)

– An auxiliary tree member of T A ⊆ A must be adjoined

DERIVATION TREES

● A derived tree does not tell how it was constructed

● The Derivation Tree specifies how a derived tree was constructed

● Both Substitution and Adjunction are considered in Derivation trees

● Substitution operations are denoted by dashed lines (- - - -)

● Adjunction operations are denoted by unbroken lines ( )

“ Yesterday a man saw Mary ”

DERIVATION TREES

Source: TAG (Joshi & Shabes 1997)

DERIVATION TREES

Source: TAG (Joshi & Shabes 1997)

LEXICALIZED GRAMMARS

Consist of:

1) Finite set of structures each associated with a lexical item (anchor)

2) Operation/s for building these structures

Linguistic interest:

Rules should not be separated totally from their lexical realization

LEXICALIZED GRAMMARS

Substitution alone is too restrictive:

- We can only add elements to the leaves of a tree

- We cannot lexicalize a tree or it doesn’t make sense linguistically (cannot freely

choose the anchors)

The power of adjoining:

- The distance between two nodes can be increased, i. e., we can insert a tree inside

of another tree (unlike substitution)

- The tree can be lexicalized (and with enough freedom to make sense linguistically)

LINGUISTIC RELEVANCE

We can increase the distance between two dependent elements and obtain long-distance

dependencies.

Example: Who did John tell Sam that Bill likes

Elementary Trees

1

Dependency

2

Derived Tree

LINGUISTIC RELEVANCE

Other examples...

Extraposition:

A relatively "heavy" constituent appears to the right of its canonical position.

Subordinate clauses:

Maria glaubt, dass Peter freundlich ist.

with red hairwas there .Some guy

APPLICATIONS OF TAG

● Can describe the language of squares, that is, of the form { yy | y {0, 1}* }∈ NT)

● Can describe languages of the form { an bn cn dn | n >= 1 }

● Lexicalization of CFGs

● Long-distance dependencies in language

SOME VARIANTS OF TAG

● Feature Structure Based TAGs

● Synchronous TAGs

● Probabilistic TAGs

● Using Description Trees in TAGs

● Multi-component TAGs (MCTAGs)

RECAP & CONCLUSION

● TAGs, Trees in TAG, Properties, Constraints

● Derivation trees

● Lexicalized Grammar

● Linguistic Relevance of TAGs

● Some applications and variants of TAGs

If you have any questions, please contact us!

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