Logic and Logical Philosophy:1-22 (forthcoming)

Francesco Paoli
Universita di Cagliari
Damian Szmuc
Universidad de Buenos Aires (UBA)
The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic.
Keywords logics of variable inclusion  significance logics  analytic entailment  weak Kleene logics  Płonka sums
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DOI 10.12775/llp.2021.015
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References found in this work BETA

Simple Hyperintensional Belief Revision.F. Berto - 2018 - Erkenntnis 84 (3):559-575.
Semantical Analysis of Weak Kleene Logics.Roberto Ciuni & Massimiliano Carrara - 2019 - Journal of Applied Non-Classical Logics 29 (1):1-36.
Logics of Nonsense and Parry Systems.Thomas Macaulay Ferguson - 2015 - Journal of Philosophical Logic 44 (1):65-80.

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Applications of Relating Semantics.Tomasz Jarmużek & Francesco Paoli - forthcoming - Logic and Logical Philosophy:1-17.

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