In 1956, Chomsky wrote, "A phrase-structure grammar is defined by a finite vocabulary (alphabet) Vp, and a finite set Σ of initial strings in Vp, and a finite set F of rules of the form: X → Y, where X and Y are strings in Vp."1
In linguistics, phrase structure grammars are all those grammars that are based on the constituency relation, as opposed to the dependency relation associated with dependency grammars; hence, phrase structure grammars are also known as constituency grammars.2 Any of several related theories for the parsing of natural language qualify as constituency grammars, and most of them have been developed from Chomsky's work, including
Further grammar frameworks and formalisms also qualify as constituency-based, although they may not think of themselves as having spawned from Chomsky's work, e.g.
Chomsky, Noam (1956). "Three models for the description of language" (PDF). IRE Transactions on Information Theory: 117. Archived from the original (PDF) on 2023-05-03. https://web.archive.org/web/20230503111934/https://chomsky.info/wp-content/uploads/195609-.pdf ↩
Matthews (1981:71ff.) provides an insightful discussion of the distinction between constituency- and dependency-based grammars. See also Allerton (1979:238f.), McCawley (1988:13), Mel'cuk (1988:12-14), Borsley (1991:30f.), Sag and Wasow (1999:421f.), van Valin (2001:86ff.). ↩