Description

• Title:
  Super-Strict Implications
• Creator:
  Gherardi, Guido;
  Orlandelli, Eugenio
• Contributor:
  Gherardi, Guido - University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy;
  Orlandelli, Eugenio - University of Bologna, Department of Philosophy and Communication Studies I-40126, Via Zamboni 38, Bologna, Italy;
  Gherardi, Guido - guido.gherardi@unibo.it;
  Orlandelli, Eugenio - eugenio.orlandelli@unibo.it
• Description:
  This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2021.05.05;
  2021.01.20
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;1;
  50
• Subject:
  Strict implication;
  paradoxes of implication;
  connexive implication;
  sequent calculi;
  structural rules
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/35350 ;
  2449-836X;
  10.18778/0138-0680.2021.02
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other