Description

• Title:
  Nested Sequent Calculi for Some Modal Logics with Non-Standard Modalities
• Creator:
  Petrukhin, Yaroslav
• Description:
  This paper introduces nested sequent calculi for modal logics that include non-standard modalities as primitive operators in their languages. By non-standard modalities, we mean non-contingency, contingency, essence, accident, impossibility, and unnecessity. We consider basic normal modal logic K and its serial, reflexive, transitive, and symmetric extensions. Our research begins by using Poggiolesi’s nested sequent calculi as a foundation. These calculi are specifically designed for logics that are formulated in a language that includes the necessity operator. Next, we proceed to modify their rules to accommodate non-standard modalities. We then establish the soundness and completeness of the resulting calculi. As a consequence, we get that the nested sequent calculus for K is cut-free. Subsequently, we provide a constructive cut admissibility proof for K. Finally, we discuss the issues pertaining to the cut admissibility for the extensions of K and their relationships with the so-called special structural rules as well as the potential for considering other forms of non-standard modalities.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2025 Yaroslav Petrukhin;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2025.04.28
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 34 No. 2 (2025): June; 287-318;
  Logic and Logical Philosophy; Tom 34 Nr 2 (2025): Czerwiec; 287-318;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/55160/42340
• Subject:
  nested sequent calculus;
  cut elimination;
  4-valued modal logics;
  contingency logic;
  essence logic;
  accident logic;
  paraconsistent logic;
  paracomplete logic
• Identifier: https://apcz.umk.pl/LLP/article/view/55160
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text