A formal system is sound if we cannot prove anything that’s wrong. This is in contrast with completeness, which is the property that you can prove all things right. 1

More formally, a proof system is sound if and only if every provable conclusion is logically entailment and provability. In other words, if , then . In contrast, a proof system is complete if and only if every logical conclusion is provable. In other words, if , then .

Not to be confused with sound argument, which operate on the scope of single arguments rather than logical systems

Footnotes

  1. incompleteness - What is the difference between Completeness and Soundness in first order logic? - Mathematics Stack Exchange