Difference between revisions of "Deductive system"
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== Description == | == Description == | ||
| − | Such a deductive system is intended to preserve deductive qualities in the formulas that are expressed in the system | + | 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 | + | 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 [[logical 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. | There should be no element of any interpretation of the language that gets involved with the deductive nature of the system. | ||
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* [[Formal system]] | * [[Formal system]] | ||
| − | * [[ | + | * [[Mathematical logic]] |
* [[Rule of inference]] | * [[Rule of inference]] | ||
Latest revision as of 09:33, 21 September 2016
In the mathematical logic of formal systems, 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 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 logical 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
External links
- Formal system # deductive system @ Wikipedia.org
