Tree-adjoining grammar (TAG) is a grammar formalism defined by Aravind Joshi and introduced in Tree-adjoining grammars are somewhat similar to context-free grammars, but the elementary unit of rewriting is the tree rather than the symbol. Whereas context-free grammars have rules for rewriting symbols as strings of other symbols, tree-adjoining grammars have rules for rewriting the nodes of trees as other trees (see tree (graph theory) and tree (data structure) ).

A Tree Adjoining Grammar (TAG) is a 5-tuple G = {Σ,NT, I,A, S} such that Σ is a finite set of terminal symbols. NT is a finite set of non terminal symbols. I is a finite set of finite trees called initial trees. A is a finite set of finite trees called auxiliary trees. S is a distinguished non-terminal symbol. The trees in I ∪ A are called elementary trees. The trees of G are combined using adjunction and substitution.

TAG Elementary trees NP John S NP↓ VP runs VP VP ⋆ ADV quickly Initial trees are elementary trees whose leaves are labelled with non terminal or terminal categories. Leaf nodes labelled with non terminal are substitution nodes marked with ↓ Auxiliary trees are elementary trees whose with a designated foot node. The root and the foot nodes are labelles with the same category.

The rules in a TAG are trees with a special leaf node known as the foot node, which is anchored to a word. There are two types of basic trees in TAG: initial trees (often represented as '') and auxiliary trees (''). Initial trees represent basic valency relations, while auxiliary trees allow for recursion. Auxiliary trees have the root (top) node and foot node labeled with the same symbol. A derivation starts with an initial tree, combining via either substitution or adjunction. Substitution replaces a frontier node with another tree whose top node has the same label. Adjunction inserts an auxiliary tree into the center of another tree. The root/foot label of the auxiliary tree must match the label of the node at which it adjoins. Other variants of TAG allow multi-component trees, trees with multiple foot nodes, and other extensions.

S VP NP NP ↓ VP VP ⋆ ADV John runs quickly S NP VP VP ADV John runs quickly Adjunction inserts an auxiliary tree into a tree (Adjunction is not allowed on substitution nodes) Substitution inserts a derived or elementary tree at the substitution node of a TAG tree.

There are several extensions of tree adjoining grammars being explored, such as lexical tree adjoining grammars (LTAGs). LTAGs consist of sets of initial and auxiliary trees which can correspond to units in human language. A TAG is lexicalized if each elementary tree has at least one leaf with a terminal label. In lexicalized TAG, each elementary tree has at least one leaf with a terminal label. Computationally interesting: if the grammar is finite, the number of analyses for a sentence is finite. Linguistically interesting: each lexical item can be associated with the set of syntactic constructions it occurs in.

Tree Adjoined Grammars fits in between the Context Free and Context Sensitive classes in the Chomsky Hierarchy: they describe Mildly Context-sensitive languages. Where as Context Free grammars have the pleasant property of being parsable in polynomial space and time, they are not adequate for describing for example the natural languages

Vijay-Shanker and Weir (1994) demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages.

Two ways of grammar implementation with TAG 1)XTAG tools (UPenn) XTAG is an on-going project to develop a wide-coverage grammar for English using a lexicalized Tree Adjoining Grammar (TAG) formalism. XTAG also serves as an system for the development of TAGs and consists of a parser, an X-windows grammar development interface and a morphological analyzer. parser, editor, viewer,... 2) XMG + TuLiPA XMG: eXtensible MetaGrammar (Duchier et al, 2004) TuLiPA: T¨ubingen Linguistic Parsing Architecture (Parmentier et al, 2008)

Grammar/ linguistic theory: rules for well-formed structures of natural language Grammar formalism: mathmatically concise description language Tree Adjoining Grammar (TAG) Implementation: (the result of) a process to translate sth. into a specific grammar formalism into a specific input format for a parser

TAG departs from other linguistic framework by its linguistic and computational properties : extended domain of locality, factoring out of recursion, mildly context-sensitive. Semantic construction in TAG is still an open research area. Surface realisation benefits from the susbtitution/adjunction distinction. Tree Adjoining Grammar is a good formalism for describing natural language syntax. Exact type of TAG, and exact type of linguistic theory, are active areas of research

A. K. Joshi. (1985). An Introduction to Tree Adjoining Grammars. Philadelphia, Pennsylvania: Technical Report MS- CIS-86-64, Univ. of Pennsylvania. Claire Gardent, Tree Adjoining Grammars Theory and Practice, Bankok, Philippe de Groote, Tree Adjoining Grammars as Abstract Categorial Grammars, Campus Scientifique, B.P. 239, France. XTAG project: /slides/gimpl intro.pdf duesseldorf.de/~lichte/events/tag/slides/1-intro.pdf