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, language, formal, formal languages":

... A process calculus is then a

**formal language**imposed on a history monoid in a consistent fashion ...

**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 ... 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 ... A

**formal**grammar determines which symbols and sets of symbols are formulas in a

**formal language**...

**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**... set of possible formulas of a particular logic is a

**formal language**, and an interpretation assigns a meaning to each of the formulas—usually, a truth value ... The study of interpretations of

**formal languages**is called

**formal**semantics ...

**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 ...

... 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 ...

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

“I am always sorry when any *language* is lost, because languages are the pedigree of nations.”

—Samuel Johnson (1709–1784)

“True variety is in that plenitude of real and unexpected elements, in the branch charged with blue flowers thrusting itself, against all expectations, from the springtime hedge which seems already too full, while the purely *formal* imitation of variety ... is but void and uniformity, that is, that which is most opposed to variety....”

—Marcel Proust (1871–1922)