Description

• Title:
  Linear Abelian Modal Logic
• Creator:
  Mohammadi, Hamzeh
• Contributor:
  Isfahan University of Technology, Department of Mathematical Sciences;
  hamzeh.mohammadi@math.iut.ac.ir
• Description:
  A many-valued modal logic, called linear abelian modal logic \(\rm {\mathbf{LK(A)}}\) is introduced as an extension of the abelian modal logic \(\rm \mathbf{K(A)}\). Abelian modal logic \(\rm \mathbf{K(A)}\) is the minimal modal extension of the logic of lattice-ordered abelian groups. The logic \(\rm \mathbf{LK(A)}\) is axiomatized by extending \(\rm \mathbf{K(A)}\) with the modal axiom schemas \(\Box(\varphi\vee\psi)\rightarrow(\Box\varphi\vee\Box\psi)\) and \((\Box\varphi\wedge\Box\psi)\rightarrow\Box(\varphi\wedge\psi)\). Completeness theorem with respect to algebraic semantics and a hypersequent calculus admitting cut-elimination are established. Finally, the correspondence between hypersequent calculi and axiomatization is investigated.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0/
• Date:
  2024.04.12;
  2023.12.15
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;1;
  53
• Subject:
  many-valued logic;
  modal logic;
  abelian logic;
  hypersequent calculus;
  cut-elimination
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/51685 ;
  2449-836X;
  10.18778/0138-0680.2023.30
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other