A deductive system (also called a deductive apparatus of a formal system) consists of the axioms (or axiom schemata) and rules of inference that can be used to derive the theorems of the system.
Such a deductive system is intended to preserve deductive qualities in the formulas that are expressed in the system. Usually the quality we are concerned with is truth as opposed to falsehood. However, other modalities, such as justification or belief may be preserved instead.
In order to sustain its deductive integrity, a deductive apparatus must be definable without reference to any intended interpretation of the language. The aim is to ensure that each line of a derivation is merely a syntactic consequence of the lines that precede it. There should be no element of any interpretation of the language that gets involved with the deductive nature of the system.
Famous quotes containing the word system:
“UG [universal grammar] may be regarded as a characterization of the genetically determined language faculty. One may think of this faculty as a ‘language acquisition device,’ an innate component of the human mind that yields a particular language through interaction with present experience, a device that converts experience into a system of knowledge attained: knowledge of one or another language.”
—Noam Chomsky (b. 1928)