HOME

TheInfoList



OR:

Tree-adjoining grammar (TAG) is a
grammar formalism In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that are valid according to the language's syntax. A grammar does not describ ...
defined by Aravind Joshi. Tree-adjoining grammars are somewhat similar to
context-free grammar In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form :A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be em ...
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) In graph theory, a tree is an undirected graph in which any two vertices are connected by ''exactly one'' path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ...
and
tree (data structure) In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be c ...
).


History

TAG originated in investigations by Joshi and his students into the family of adjunction grammars (AG), the "string grammar" of
Zellig Harris Zellig Sabbettai Harris (; October 23, 1909 – May 22, 1992) was an influential American linguistics, linguist, mathematical syntactician, and methodologist of science. Originally a Semitic languages, Semiticist, he is best known for his work i ...
. AGs handle exocentric properties of language in a natural and effective way, but do not have a good characterization of endocentric 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-Schützenberger hierarchy but intersects it in interesting and linguistically relevant ways. The center strings and adjunct strings can also be generated by a
dependency grammar Dependency grammar (DG) is a class of modern grammatical theories that are all based on the dependency relation (as opposed to the ''constituency relation'' of phrase structure) and that can be traced back primarily to the work of Lucien Tesni� ...
, avoiding the limitations of rewrite systems entirely.


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 '\alpha') and ''auxiliary'' trees ('\beta'). 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. The root/foot label of the auxiliary tree must match the label of the node at which it adjoins. Adjunction can thus have the effect of inserting an auxiliary tree into the center of another tree. Other variants of TAG allow multi-component trees, trees with multiple foot nodes, and other extensions.


Complexity and application

Tree-adjoining grammars are more powerful (in terms of weak generative capacity) than
context-free grammar In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form :A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be em ...
s, but less powerful than
linear context-free rewriting system Generalized context-free grammar (GCFG) is a grammar formalism that expands on context-free grammars by adding potentially non-context-free composition functions to rewrite rules. Head grammar (and its weak equivalents) is an instance of such a GC ...
s,Kallmeyer, Laura (2010). Parsing Beyond Context-Free Grammars. Springer. Here: p.215-216 indexedsince for each tree-adjoining grammar, a linear indexed grammar can be found producing the same language, see
below Below may refer to: *Earth * Ground (disambiguation) *Soil *Floor * Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Ernst von Below (1863–1955), German World War I general *Fred Below ...
, and for the latter, a weakly equivalent (proper) indexed grammar can be found, in turn, see Indexed grammar#Computational Power
or context-sensitive grammars. A TAG can describe the language of squares (in which some arbitrary string is repeated), and the language \. This type of processing can be represented by an
embedded pushdown automaton An embedded pushdown automaton or EPDA is a computational model for parsing languages generated by tree-adjoining grammars (TAGs). It is similar to the context-free grammar-parsing pushdown automaton, but instead of using a plain stack to store sym ...
. 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, tree-adjoining grammars are often described as mildly context-sensitive. These grammar classes are conjectured to be powerful enough to model
natural language In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...
s while remaining efficiently parsable in the general case.


Equivalences

Vijay-Shanker and Weir (1994)Vijay-Shanker, K. and Weir, David J. 1994. ''The Equivalence of Four Extensions of Context-Free Grammars''. Mathematical Systems Theory 27(6): 511–546. demonstrate that
linear indexed grammars Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear re ...
,
combinatory categorial grammar Combinatory categorial grammar (CCG) is an efficiently parsable, yet linguistically expressive grammar formalism. It has a transparent interface between surface syntax and underlying semantic representation, including predicate–argument structur ...
, tree-adjoining grammars, and
head grammar Head grammar (HG) is a grammar formalism introduced in Carl Pollard (1984) Pollard, C. 1984. ''Generalized Phrase Structure Grammars, Head Grammars, and Natural Language''. Ph.D. thesis, Stanford University, CA. as an extension of the context-fr ...
s are weakly equivalent formalisms, in that they all define the same string languages.


Lexicalized

Lexicalized tree-adjoining grammars (LTAG) are a variant of TAG in which each elementary tree (initial or auxiliary) is associated with a lexical item. A lexicalized grammar for English has been developed by the XTAG Research Group of the Institute for Research in Cognitive Science at the University of Pennsylvania.


Notes


References


External links


The XTAG project
which uses a TAG for natural language processing.
SemConst Documentation
A quick survey on Syntax and Semantic Interface problematic within the TAG framework.
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 grammars with
tree tuple In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are u ...
s
The Metagrammar Toolkit
which provides several tools to edit and compile MetaGrammars into TAGs. It also include a wide coverage French Metagrammars.
LLP2
A
lexicalized tree adjoining grammar In linguistics, lexicalization is the process of adding words, set phrases, or word patterns to a language's lexicon. Whether '' word formation'' and ''lexicalization'' refer to the same process is controversial within the field of linguistics. ...
parser which provides an easy to use graphical environment (page in French) {{DEFAULTSORT:Tree-Adjoining Grammar Generative linguistics Grammar frameworks