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arXiv · 1809.06761

Containment logics: algebraic completeness and axiomatization

Stefano Bonzio·Michele Pra Baldi
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Abstract

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.

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Stefano Bonzio, Michele Pra Baldi. 2018-09-18. Containment logics: algebraic completeness and axiomatization. https://arxiv.org/abs/1809.06761

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