soundness theorem

The soundness theorem in logic means that if a statement can be proven true using a set of logical rules, then it is indeed true in every possible real-world interpretation or situation. In other words, the rules of the system are reliable: they don't lead us to prove false statements as true. This ensures that the conclusions derived are trustworthy, as the proof process aligns with actual truth. It's a guarantee that our logical reasoning system doesn't produce errors, maintaining consistency between what can be proven and what is genuinely true.