# Metalogic - Overview - Formal Language

A formal language is an organized set of symbols the essential feature of which is that it can be precisely defined in terms of just the shapes and locations of those symbols. Such a language can be defined, then, without any reference to any meanings of any of its expressions; it can exist before any interpretation is assigned to it—that is, before it has any meaning. First order logic is expressed in some formal language. A formal grammar determines which symbols and sets of symbols are formulas in a formal language.

A formal language can be defined formally as a set A of strings (finite sequences) on a fixed alphabet α. Some authors, including Carnap, define the language as the ordered pair <α, A>. Carnap also requires that each element of α must occur in at least one string in A.

### Other articles related to "formal language, formal languages, language, formal":

Process Calculus - Relationship To Other Models of Concurrency
... A process calculus is then a formal language imposed on a history monoid in a consistent fashion ... Thus, a process calculus is to a history monoid what a formal language is to a free monoid (a formal language is a subset of the set of all possible finite-length ...
Formal Language - Applications - Formal Theories, Systems and Proofs - Interpretations and Models
... Formal languages are entirely syntactic in nature but may be given semantics that give meaning to the elements of the language ... For instance, in mathematical logic, the set of possible formulas of a particular logic is a formal language, and an interpretation assigns a meaning to each of the formulas—usuall ... The study of interpretations of formal languages is called formal semantics ...
Process Calculi - Relationship To Other Models of Concurrency
... A process calculus is then a formal language imposed on a history monoid in a consistent fashion ... Thus, a process calculus is to a history monoid what a formal language is to a free monoid (a formal language is a subset of the set of all possible finite-length strings of an alphabet generated by the Kleene star) ...
Formation Rule - Formal Language
... A formal language is an organized set of symbols the essential feature being that it can be precisely defined in terms of just the shapes and locations of those symbols ... Such a language can be defined, then, without any reference to any meanings of any of its expressions it can exist before any interpretation is assigned to ... A formal grammar determines which symbols and sets of symbols are formulas in a formal language ...
Lithuanian Name - Formal and Informal Use - Formal Language - Given Name / Surname Order
... The given name(s) normally comes before the surname ... However, in a list of people sorted alphabetically by surname, the surname usually comes first ...

### Famous quotes containing the words language and/or formal:

in every language even deafanddumb
thy sons acclaim your glorious name by gorry
by jing by gee by gosh by gum
—E.E. (Edward Estlin)

It is in the nature of allegory, as opposed to symbolism, to beg the question of absolute reality. The allegorist avails himself of a formal correspondence between “ideas” and “things,” both of which he assumes as given; he need not inquire whether either sphere is “real” or whether, in the final analysis, reality consists in their interaction.
Charles, Jr. Feidelson, U.S. educator, critic. Symbolism and American Literature, ch. 1, University of Chicago Press (1953)