Pure Variable Inclusion Logics
DOI:
https://doi.org/10.12775/LLP.2021.015Słowa kluczowe
logics of variable inclusion, significance logics, analytic entailment, weak Kleene logics, Płonka sumsAbstrakt
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.
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Prawa autorskie (c) 2021 Francesco Paoli, Michele Pra Baldi, Damian Szmuc
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
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