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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]]

Revision as of 16:34, 2 February 2014

Tree-adjoining grammar (TAG) is a grammar formalism defined by Aravind Joshi. 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)).

History

TAG originated in investigations by Joshi and his students into the family of adjunction grammars (AG),[1] 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 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.[2]

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 'α') and auxiliary trees ('β'). Initial trees represent basic valency relations, while auxiliary trees allow for recursion.[3] 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.[4] 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.

Complexity and application

Tree-adjoining grammars are often described as 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 or context-sensitive grammars. Mildly context-sensitive grammars are conjectured to be powerful enough to model natural languages while remaining efficiently parsable in the general case.[5]

A TAG can describe the language of squares (in which some arbitrary string is repeated), and the language {anbncndn|1≤n}. 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 languages.

Equivalences

Vijay-Shanker and Weir (1994)[6] 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.

References

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  1. ↑ Template:Cite paper
  2. ↑ Template:Cite paper
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  6. ↑ Vijay-Shanker, K. and Weir, David J. 1994. The Equivalence of Four Extensions of Context-Free Grammars. Mathematical Systems Theory 27(6): 511–546.
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