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.

本文研究了逻辑\（\ vdash \）的包含伴侣（或右变量包含伴侣）。这由结果关系\（\ vdash ^ {r} \）组成，该结果关系满足\（\ vdash \）的所有推论，其中结论的变量包含在前提集的那些变量中（如果不是）不一致。根据[10]中开始的工作，我们表明从代数到逻辑矩阵的Płonkasum构造的不同概括，可以为包含逻辑提供基于矩阵的语义。特别是，我们为广泛的包含逻辑系列提供了一个适当的完备性定理，并且展示了如何产生完整的希尔伯特风格公理化。