SOUNDNESS

Soundness

In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formulas that are valid with respect to its semantics. In most cases, this comes down to its rules having the property of preserving truth, but this is not the case in general.

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soundness

Noun

  1. The state or quality of being sound.
  2. The result or product of being sound.
  3. The property (of an argument) of not only being valid, but also of having true premises.
  4. The property of a logical theory that whenever a wff is a theorem then it must also be valid. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever <math> T \vdash \phi</math> is true, then <math> T \vDash \phi</math> must also be true, for any wff φ of logic L.


The above text is a snippet from Wiktionary: soundness
and as such is available under the Creative Commons Attribution/Share-Alike License.

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