# Grammar, transformational

A formal grammar (cf. Grammar, formal). A transformational grammar is used for the transformation of syntactic structures (cf. Syntactic structure); this renders them better suited for the description of natural language than formal grammars of other types, which generate or recognize syntactic structures only together with the generation (recognition) of strings, since a separate recognition of syntactic and linear relations between speech units is in better agreement with the nature of language.

Transformational grammars are much more cumbersome than grammars which operate by transformation of "strings" , as a result of which the development of the formal concept of a transformational grammar only began in the late 1960s, even though its fundamentals had been laid by N. Chomsky some ten years earlier. There are several concepts of transformational grammars; some of them are intended for processing component systems, others for processing hierarchy trees. As an example, one can quote the so-called $ \Delta $- grammars, which are finite systems of elementary transformations of the form $ t _ {1} \Rightarrow t _ {2} \mid f $, where $ t _ {1} $ and $ t _ {2} $ are (finite) oriented trees with marked vertices and arcs and $ f $ is a mapping of a set of vertices of $ t _ {1} $ into a set of vertices of $ t _ {2} $. To apply such a transformation to a tree $ T $( interpreted as a hierarchy tree) with marked vertices and arcs means to replace some subtree in it that is isomorphic to $ t _ {1} $ by a subtree that is isomorphic to $ t _ {2} $, while "hanging up" the "external links" of each vertex $ A $ of the tree which is being replaced onto the vertex $ f( A) $ of the replacing tree. $ \Delta $- grammars are used to effect the transition from syntactic structures on one level to syntactic structures on another level (cf. Mathematical linguistics) and to effect synonymous transformations of deep syntactic structures.

#### References

[1] | N. Chomsky, , News in linguistics (1962) pp. 412–527 (In Russian) |

[2] | S. Ginsburg, B. Partee, "A mathematical model of transformational grammars" Inform. and Control , 15 (1969) pp. 297–334 |

[3] | A.V. Gladkii, I.A. Mel'chuk, , Informational questions of semiotics, linguistics and automatic translation : 1 , Moscow (1971) pp. 16–41 (In Russian) |

#### Comments

Another mathematical model for transformational grammars can be found in [a1]. The basic publication of Chomsky on transformational grammars is [a2]. The grammatical model presently followed in the Chomsky school is not transformational grammar any more but so-called "gouvernment and binding theorygouvernment and binding theory" , see [a3]. Although it has some properties in common with transformational grammar, it is not even a generative grammar (cf. Grammar, generative).

See also Formal languages and automata.

#### References

[a1] | P.S. Peters, R.W. Ritchie, "On the generative power of transformational grammars" Information Sciences , 6 (1973) pp. 49–83 |

[a2] | N. Chomsky, "Aspects of the theory of syntax" , M.I.T. (1965) |

[a3] | N. Chomsky, "Lectures on gouvernment and binding" , Foris , Dordrecht (1981) |

[a4] | E. Bach, "An introduction to transformational grammars" , Holt, Rinehart & Winston (1964) |

**How to Cite This Entry:**

Grammar, transformational.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Grammar,_transformational&oldid=47120