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formal language[¦fȯr·məl ′laŋ·gwij]
(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.