  The classical condition "$\phi$ is a semantic consequence of $\Theta$" in
infinite-valued propositional \L ukasiewicz logic \L$_\infty$ is refined using
enriched valuations that take into account the effect on $\phi$ of the
stability of the truth-value of all $\theta\in \Theta$ under small
perturbations (or, measurement errors) of the models of $\Theta$. The
differential properties of the functions represented by $\phi$ and by all
$\theta\in \Theta$ naturally lead to a new notion of semantic consequence
$\models_\partial$ that turns out to coincide with syntactic consequence
$\vdash$.
