A theory of negation so that for a formula $\phi$, the content of its negation $\neg \phi$ ‘cancels’ that of $\phi$, entailing that a conjunction $\phi \wedge \neg \phi$ or an inconsistent set of premisses has no content, i.e., entails nothing. If the claim that an inconsistent set of formulae $\Gamma$ is construed as the property that $\Gamma$ has no consequences, then a deductive system with a cancellation negation will not observe the principle of explosion. Hence, cancellation negation is an example of a semantic notion that leads to paraconsistent logic independently of, e.g., considerations of dialetheism.