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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]
A formal language is a language that is defined by a formal system. Like languages in linguistics , formal languages generally have two aspects: the syntax is what the language looks like (more formally: the set of possible expressions that are valid utterances in the language)
The word name is possibly derived from the Proto-Indo-European language hypothesised word nomn. [27] The distinction between names and nouns, if made at all, is extremely subtle, [28] although clearly noun refers to names as lexical categories and their function within the context of language, [29] rather that as "labels" for objects and ...
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 ...
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 ...
The idea behind this step is that the regular terms still carry their original meaning and thereby make it easier to understand the formulas and to see how they relate to the original text. The natural language vocabulary is usually not precisely defined and therefore lacks the exactness demanded by formal logic. [87]
Let us notate a formal grammar as = (,,,), with a set of nonterminal symbols, a set of terminal symbols, a set of production rules, and the start symbol.. A string () directly yields, or directly derives to, a string (), denoted as , if v can be obtained from u by an application of some production rule in P, that is, if = and =, where () is a production rule, and , is the unaffected left and ...