Description

• Title:
  S5-Style Non-Standard Modalities in a Hypersequent Framework
• Creator:
  Petrukhin, Yaroslav
• Description:
  The aim of the paper is to present some non-standard modalities (such as non-contingency, contingency, essence and accident) based on S5-models in a framework of cut-free hypersequent calculi. We also study negated modalities, i.e. negated necessity and negated possibility, which produce paraconsistent and paracomplete negations respectively. As a basis for our calculi, we use Restall's cut-free hypersequent calculus for S5. We modify its rules for the above-mentioned modalities and prove strong soundness and completeness theorems by a Hintikka-style argument. As a consequence, we obtain a cut admissibility theorem. Finally, we present a constructive syntactic proof of cut elimination theorem.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2021 Logic and Logical Philosophy
• Date:
  2021.12.16
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 31 No. 3 (2022): September; 427-456;
  Logic and Logical Philosophy; Tom 31 Nr 3 (2022): Wrzesień; 427-456;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/33865/30823
• Subject:
  hypersequent calculus;
  cut elimination;
  proof theory;
  modal logic;
  contingency logic;
  essence logic;
  accident logic
• Identifier: https://apcz.umk.pl/LLP/article/view/33865
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text