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Mathematics > Logic

arXiv:1809.06761 (math)
[Submitted on 18 Sep 2018 (v1), last revised 4 May 2020 (this version, v2)]

Title:Containment logics: algebraic completeness and axiomatization

Authors: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 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.
Subjects: Logic (math.LO)
Cite as: arXiv:1809.06761 [math.LO]
  (or arXiv:1809.06761v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1809.06761

Submission history

From: Stefano Bonzio [view email]
[v1] Tue, 18 Sep 2018 14:22:48 UTC (40 KB)
[v2] Mon, 4 May 2020 11:01:45 UTC (29 KB)
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