Deductive system - Revision history

Karl Jones: /* See also */

2016-09-21T16:33:09Z

‎See also

Karl Jones: /* Description */

2016-09-13T16:31:56Z

‎Description

Karl Jones: Created page with "In the mathematical logic of formal systems, a '''deductive system''' (also called a deductive apparatus of a formal system) consists of the Axiom|axio..."

2016-09-13T15:59:19Z

Created page with "In the mathematical logic of formal systems, a '''deductive system''' (also called a deductive apparatus of a formal system) consists of the Axiom|axio..."

New page

In the [[mathematical logic]] of [[Formal system|formal systems]], a '''deductive system''' (also called a deductive apparatus of a formal system) consists of the [[Axiom|axioms]] (or [[Axiom schema|axiom schemata]]) and [[Rule of inference|rules of inference]] that can be used to [[Formal proof|derive a formal proof]] of the theorems of the system.

== Description ==

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.

== See also ==

* [[Formal system]]
* [[mathematical logic]]
* [[Rule of inference]]

== External links ==

* [https://en.wikipedia.org/wiki/Formal_system#Deductive_system Formal system # deductive system] @ Wikipedia.org

[[Category:Logic]]

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 * [[Formal system]]
-* [[mathematical logic]]
+* [[Mathematical logic]]
 * [[Rule of inference]]

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 == Description ==
-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.
+Such a deductive system is intended to preserve deductive qualities in the formulas that are expressed in the system.
-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.
+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.
 There should be no element of any interpretation of the language that gets involved with the deductive nature of the system.