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Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas. A formal grammar is a set of rules for rewriting strings, along with a "start symbol ...
The formal study of grammar is an important part of children's schooling from a young age through advanced learning, though the rules taught in schools are not a "grammar" in the sense that most linguists use, particularly as they are prescriptive in intent rather than descriptive.
A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules , which may be interpreted as valid rules of inference, or a set of axioms , or have both.
The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a language's vocabulary (or alphabet) that are valid according to the language's syntax. The linguist Noam Chomsky theorized that four ...
English grammar is the set of structural rules of the English language. ... government, and news, over a range of registers, from formal to informal.
Rudolph Carnap defined the meaning of the adjective formal in 1934 as follows: "A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for example, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are ...
Formal linguistics is the branch of linguistics which uses applied mathematical methods for the analysis of natural languages. Such methods include formal languages , formal grammars and first-order logical expressions.
Formal language, comprising the symbolic "words" or "sentences" of a formal system; Formal grammar, a grammar describing a formal language; Colloquialism, the linguistic style used for informal communication; T–V distinction, involving a distinction between formal and informal words for "you" Formal proof, a fully rigorous proof as is ...