Grammars

Grammars describe the rules by which the elements of a language can be combined. In linguistics, a grammar is a descriptive system that accounts for how sentences are formed in a natural language, including word order, agreement, and sentence structure. In formal language theory, a grammar specifies how to generate the strings that belong to a formal language.

A grammar consists of a set of symbols, a set of production rules, a subset called terminals, a subset of nonterminals, and a designated start symbol. Production rules replace nonterminal symbols with sequences of terminals and nonterminals. The strings produced by repeatedly applying rules from the start symbol form the language described by the grammar.

In linguistics, grammars may be descriptive, encoding speakers’ tacit knowledge, or prescriptive, prescribing preferred forms. Generative grammars aim to capture the underlying structure of language, often using transformations to relate deep representations to surface forms. In formal language theory, grammars are analyzed via automata and computational resources, leading to classifications such as regular, context-free, context-sensitive, and recursively enumerable grammars.

Applications include programming language design, where parsers are built from context-free grammars; natural language processing, where grammars support parsing and interpretation; and theory, where grammars help formalize notions of syntax and complexity. Ambiguities in natural language grammars pose challenges for interpretation and automatic parsing.

Historically, formal grammars emerged in the 1950s and 1960s with Noam Chomsky’s work on generative grammar and the development of the Chomsky hierarchy.