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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 ...
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules called a formal grammar. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings called words. [1]
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 linguistics also forms the basis of computational linguistics.
In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is distinguished from strong (or structural) equivalence, which additionally means that the two parse trees [clarification needed] are reasonably similar in that the same semantic interpretation can be ...
Any language that one uses to talk about a formal system is called a metalanguage. The metalanguage may be a natural language, or it may be partially formalized itself, but it is generally less completely formalized than the formal language component of the formal system under examination, which is then called the object language , that is, the ...
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.
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 ...
C. Categorial grammar; Chomsky hierarchy; Chomsky normal form; Chomsky–Schützenberger enumeration theorem; Chomsky–Schützenberger representation theorem