Containment Logics: Algebraic Completeness and Axiomatization

Studia Logica 109 (5):969-994 (2021)
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The paper studies the containment companion of a logic \. This consists of the consequence relation \ which satisfies all the inferences of \, 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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Stefano Bonzio
University of Turin