Open AccessPure Variable Inclusion Logics
Author(s) -
Francesco Paoli,
Michele Pra Baldi,
Damián Enrique Szmuc
Publication year - 2021
Publication title -
logic and logical philosophy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.416
H-Index - 10
eISSN - 2300-9802
pISSN - 1425-3305
DOI - 10.12775/llp.2021.015
Subject(s) - finitary , t norm fuzzy logics , monoidal t norm logic , variable (mathematics) , mathematics , propositional calculus , semilattice , falsity , inclusion (mineral) , matrix (chemical analysis) , tautology (logic) , computer science , pure mathematics , algebra over a field , discrete mathematics , propositional variable , theoretical computer science , epistemology , description logic , intermediate logic , artificial intelligence , fuzzy logic , philosophy , fuzzy set , psychology , mathematical analysis , semigroup , materials science , membership function , composite material , fuzzy number , social psychology
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.