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A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules , which may be interpreted as valid rules of inference, or a set of axioms , or have both.
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 ...
Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal ...
[2] [3] In this view, language is regarded as arising from a mathematical relationship between meaning and form. The formal description of language was further developed by linguists including J. R. Firth and Simon Dik, giving rise to modern grammatical frameworks such as systemic functional linguistics and functional discourse grammar.
In sociolinguistics, a register is a variety of language used for a particular purpose or particular communicative situation. For example, when speaking officially or in a public setting, an English speaker may be more likely to follow prescriptive norms for formal usage than in a casual setting, for example, by pronouncing words ending in -ing with a velar nasal instead of an alveolar nasal ...
Formal grammar, a grammar describing a formal language; Colloquialism, the linguistic style used for informal communication; T–V distinction, involving a distinction between formal and informal words for "you" Formal proof, a fully rigorous proof as is possible only in a formal system; Dynamic and formal equivalence word-for-word translation ...
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 ...
Formal theories of grammar seek to define the different elements of language and describe the way they relate to each other as systems of formal rules or operations, while functional theories seek to define the functions performed by language and then relate them to the linguistic elements that carry them out.