Formal Language

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formal language

[¦fȯr·məl ′laŋ·gwij]
(computer science)
An abstract mathematical object used to model the syntax of a programming or natural language.

Formal Language


(1) In a broad sense, a formal language is a set of in some way specialized linguistic means that is provided with more or less precisely defined rules for forming expressions (the syntax of the formal language) and for assigning meaning to the expressions (the semantics of the language). Generally speaking, this use of the term “formal language” does not assume any special restrictions on the syntactic structure, semantic rules, or purpose of the language. For example, the expressions “H2O,” voda, eau, “water,” Wasser, and vesi can, in principle, be considered in equal measure elements of the formal language of chemistry.

(2) In logic, a formal, or formalized, language is an interpreted calculus, that is, a formal system with an interpretation. The use of formal languages is characteristic of mathematical logic, which is often defined as “the subject of formal logic as studied through the construction of formal languages.” It should, however, be noted that this definition is by no means an inherent attribute of presentations of mathematical logic. The concept of formal language not only does not generally occur in particular logico-mathematical languages but, strictly speaking, is not even an element of any specific metalanguages. It is, rather, a useful working term in preliminary heuristic elucidations of the subject matter of mathematical logic.


Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. Introduction (subsecs. 00–09). Translated from English.
References in periodicals archive ?
Since every expression of PM is associated with a particular Godel number, a meta-mathematical statement about formal expressions and their typographical relations to one another may be construed as a statement about the corresponding Godel numbers and their arithmetical relations to one another.
Logic, which made its debut at the SHK Essen in 2006, has adopted the formal expression of the Tara Classic single-lever mixer tap, but has radically stretched the design and made it more erect.
In other ways, it was the very personal response of writers who incorporated popular taste into a distinct personal formal expression.
Nowadays the solution of a task 2-like problem is represented by the construction of a numerical expression that interprets the theoretic arithmetic situation, and by means of a deductive chain of symbolic transformations aims at reflecting the structure of the property one wants to demonstrate in the structure of the formal expression.
Kirklees has already submitted a formal expression of interest to the Government's Casino Advisory Panel.
It goes without saying that what one inevitably misses in such written leavings is the electric wit and sardonic humour of this anti-democratic but never inegalitarian individual who inaugurated our tradition of numbering each issue of Umbr(a) as One--not only as a token of what he once called the 'arduous' procedure of counting to Two but also as a formal expression of fidelity to what had escaped the previous issue's 'count'.
The nineteenth century witnessed the arrival of the most significant pieces of legislation against interpersonal violence, for example, giving formal expression to ideas that had been merely percolating in the previous century.
It found its first formal expression in the creation of the Arab League in 1945, which gave a single voice to newly independent Arab states after World War II.
The idea that painting was somehow bound to fail--a presupposition that finds formal expression in the now-prevalent "deskilled" aesthetic--is also worked through in deeper conceptual terms in the canvases of Tuymans and those in his wake.
In Botta's own words "architecture and the organization of mankind's living space still represent the formal expression of history.
The operator of Singapore's Changi airport also indicated that it had not submitted a formal expression of interest due to a 5% ownership cap.
For six days there was no formal expression of regret from Pacifica's board.

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