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'''Tree-adjoining grammar (TAG)''' is a [[grammar formalism]] defined by [[Aravind Joshi]]. Tree-adjoining grammars are somewhat similar to [[context-free grammar]]s, 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)]]).
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==History==
TAG originated in investigations by Joshi and his students into the family of adjunction grammars (AG),<ref name="JoshiKosarajuYamada1969">{{cite paper
| last = Joshi
| first = Aravind
| coauthors =  S. R. Kosaraju, H. Yamada
| title = String Adjunct Grammars
| year = 1969
| publisher = Proceedings Tenth Annual Symposium on Automata Theory, Waterloo, Canada }}</ref>  
the "string grammar" of [[Zellig Harris]]. AGs handle [[endocentric]] properties of language in a natural and effective way, but do not have a good characterization of [[exocentric]] constructions; the converse is true of [[rewrite rule|rewrite grammars]], or [[phrase-structure grammar]] (PSG). In 1969, Joshi introduced a family of grammars that exploits this complementarity by mixing the two types of rules. A few very simple rewrite rules suffice to generate the vocabulary of strings for adjunction rules. This family is distinct from the [[Chomsky hierarchy]] but intersects it in interesting and linguistically relevant ways.<ref name="Joshi1969">{{cite paper
| last = Joshi
| first = Aravind
| title = Properties of Formal Grammars with Mixed Types of Rules and Their Linguistic Relevance
| year = 1969
| publisher = Proceedings Third International Symposium on Computational Linguistics, Stockholm, Sweden }}</ref>
 
==Description==
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 '<math>\alpha</math>') and ''auxiliary'' trees ('<math>\beta</math>').  Initial trees represent basic valency relations, while auxiliary trees allow for recursion.<ref name="jurafsky-martin2000">{{cite book
| last = Jurafsky
| first = Daniel
| coauthors = James H. Martin
| title = Speech and Language Processing
| year = 2000
| pages = 354
| publisher = Prentice Hall
| location = Upper Saddle River, NJ }}</ref>
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.<ref name="joshi-rambow2003">{{cite conference
| last = Joshi
| first = Aravind
| coauthors = Owen Rambow
| title = A Formalism for Dependency Grammar Based on Tree Adjoining Grammar
| year = 2003
| booktitle = Proceedings of the Conference on Meaning-Text Theory
| url = http://www1.cs.columbia.edu/~rambow/papers/joshi-rambow-2003.pdf}}</ref>
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 tree adjoining grammars|multi-component trees]], trees with multiple foot nodes, and other extensions.
 
==Complexity and application==
 
Tree-adjoining grammars are often described as [[Mildly context-sensitive grammar|mildly context-sensitive]], meaning that they possess certain properties that make them more powerful (in terms of [[weak generative capacity]]) than context-free grammars, but less powerful than [[indexed grammar|indexed]] or [[context-sensitive grammar]]s.  Mildly context-sensitive grammars are conjectured to be powerful enough to model [[natural language]]s while remaining efficiently [[parser|parsable]] in the general case.<ref name="joshi1985">{{cite book
| last = Joshi
| first = Aravind
| chapter = How much context-sensitivity is necessary for characterizing structural descriptions
| year = 1985
| publisher = Cambridge University Press
| pages = 206–250
| title = Natural Language Processing: Theoretical, Computational, and Psychological Perspectives
| editor = D. Dowty, L. Karttunen, and A. Zwicky, (eds.)
| location = New York, NY }}</ref>
 
A TAG can describe the language of squares (in which some arbitrary string is repeated), and the language <math>\{a^n b^n c^n d^n | 1 \le n \}</math>. This type of processing can be represented by an [[embedded pushdown automaton]].
 
Languages with cubes (i.e. triplicated strings) or with more than four distinct character strings of equal length cannot be generated by tree-adjoining grammars.
 
For these reasons, languages generated by tree-adjoining grammars are referred to as ''[[mildly context-sensitive language]]''s.
 
===Equivalences===
 
Vijay-Shanker and Weir (1994)<ref name="vijayshankarAndWeir1995">Vijay-Shanker, K. and Weir, David J. 1994. ''The Equivalence of Four Extensions of Context-Free Grammars''. Mathematical Systems Theory 27(6): 511–546.</ref> demonstrates that [[Indexed grammar#Linear indexed grammars|Linear Indexed Grammars]], [[Combinatory categorial grammar|Combinatory Categorial Grammars]], Tree-adjoining Grammars, and [[Head grammar|Head Grammars]] are [[Weak equivalence (formal languages)|weakly equivalent]] formalisms, in that they all define the same string languages.
 
==References==
{{Reflist}}
 
==External links==
*[http://www.cis.upenn.edu/~xtag/ The XTAG project], which uses a TAG for natural language processing.
*[http://www.let.rug.nl/~vannoord/papers/diss/diss/node59.html A tutorial on TAG]
*[http://www.computing.dcu.ie/~yguo/doc/talk/TAG.pdf Another tutorial] with focus on comparison with [[Lexical Functional Grammar]] and grammars extraction from [[Treebank]]
*[http://wiki.loria.fr/wiki/SemConst/Documentation#Background SemConst Documentation] A quick survey on Syntax and Semantic Interface problematic within the TAG framework.
*[http://sourcesup.cru.fr/tulipa/ The TuLiPa project] The Tübingen Linguistic Parsing Architecture (TuLiPA) is a multi-formalism syntactic (and semantic) parsing environment, designed mainly for [[multi-component tree adjoining grammar]]s with [[tree tuple]]s
*[http://mgkit.gforge.inria.fr/ The Metagrammar Toolkit] which provides several tools to edit and compile [[MetaGrammars]] into TAGs. It also include a wide coverage French Metagrammars.
*[http://www.loria.fr/~azim/LLP2/help/fr/index.html LLP2] A [[lexicalized tree adjoining grammar]] parser which provides an  easy to use graphical environment (page in French)
 
{{Formal languages and grammars}}
 
{{DEFAULTSORT:Tree-Adjoining Grammar}}
[[Category:Generative linguistics]]
[[Category:Grammar frameworks]]

Latest revision as of 19:03, 3 January 2015

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