Deductive system: Difference between revisions

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+#REDIRECT [[Formal system#Deductive system]]
-The '''deductive apparatus''' of a [[formal system]] consists of the [[axiom]]s (or [[axiom schema]]ta) and [[rules of inference]] that can be used to derive (prove) the [[theorem]]s of the system.<ref>Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971</ref>
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-Such a deductive system is intended to preserve [[deduction|deductive]] qualities in the [[formula (mathematical logic)|formula]]s that are expressed in the system. Usually the quality we are concerned with is [[truth]] as opposed to falsehood. However, other [[modal logic|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 [[Mathematical_proof|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.
-== See also ==
-* [[Formal grammar]]
-== References ==
-{{reflist}}
-[[Category:Syntax]]
-[[Category:Proof theory]]
-[[Category:Formal languages]]