  The paper studies the containment companion of a logic $\vdash$. This
consists of the consequence relation $\vdash^{r}$ which satisfies all the
inferences of $\vdash$, where the variables of the conclusion are
\emph{contained} into those of the (set of) premises. In accordance with our
previous work on logics of left variable inclusion, we show that a different
generalization of the P\l onka sum construction, adapted from algebras to
logical matrices, allows us to provide a matrix-based semantics for containment
logics. In particular, we provide an appropriate completeness theorem for a
wide family of containment logics, and we show how to produce a complete
Hilbert style axiomatization.
