Abstract
The paper studies the containment companion (or, right variable inclusion 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 contained into those of the set of premises, in case this is not inconsistent. In accordance with the work started in [10], we show that a different generalization of the Płonka sum construction, adapted from algebras to logical matrices, allows 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.
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