 Soundness says that if the sentence \(\beta\) is a derivable consequence of \(\alpha\), then no matter how the non-logical vocabulary of \(\mathbf{L}\) are interpreted, \(\beta\) is true in all the worlds in which \(\alpha\) true. That is to say that from true premises, our consequence relation always derives true conclusions. Soundness also implies that every theorem is valid. Soundness is a basic requirement of any  deductive consequence relation, and illustrates the intended connection between deductive proof and semantic entailment.