2018/09/18 by Bonzio, Stefano, Baldi, Michele Pra
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1809.06761
The paper studies the containment companion of a logic \vdash. This consists of the consequence relation \vdashr which satisfies all the inferences of \vdash, where the variables of the conclusion are 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 Płonka 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.