Description

• Title:
  The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)
• Creator:
  Szmuc, Damian E.
• Contributor:
  IIF, CONICET-SADAF, C1176ABL, Bulnes 642, Buenos Aires, Argentina; University of Buenos Aires, Department of Philosophy;
  szmucdamian@gmail.com
• Description:
  We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined in terms of a \(p\)-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2022.03.10;
  2021.05.27
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;4;
  50
• Subject:
  Relevant logics;
  non-transitive logics;
  p-matrix;
  weak Kleene algebra;
  infectious logics
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/41065 ;
  2449-836X;
  10.18778/0138-0680.2021.08
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other