Containment Logics: Algebraic Completeness and Axiomatization
Bonzio S.
First
;Pra Baldi M.
2021-01-01
Abstract
The paper studies the containment companion (or, right variable inclusion companion) of a logic ⊢. This consists of the consequence relation ⊢ r 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.File | Size | Format | |
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Bonzio-PraBaldi2_Containment.pdf open access
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