Description

• Title:
  Some Logics in the Vicinity of Interpretability Logics
• Creator:
  Celani, Sergio A.
• Contributor:
  Universidad Nacional del Centro and CONICET, Departamento de Matem´atica, Tandil, Argentina;
  scelani@exa.unicen.edu.ar
• Description:
  In this paper we shall define semantically some families of propositional modal logics related to the interpretability logic \(\mathbf{IL}\). We will introduce the logics \(\mathbf{BIL}\) and \(\mathbf{BIL}^{+}\) in the propositional language with a modal operator \(\square\) and a binary operator \(\Rightarrow\) such that \(\mathbf{BIL}\subseteq\mathbf{BIL}^{+}\subseteq\mathbf{IL}\). The logic \(\mathbf{BIL}\) is generated by the relational structures \(\left<X,R,N\right>\), called basic frames, where \(\left<X,R\right>\) is a Kripke frame and \(\left<X,N\right>\) is a neighborhood frame. We will prove that the logic \(\mathbf{BIL}^{+}\) is generated by the basic frames where the binary relation \(R\) is definable by the neighborhood relation \(N\) and, therefore, the neighborhood semantics is suitable to study the logic \(\mathbf{BIL}^{+}\) and its extensions. We shall also study some axiomatic extensions of \(\mathsf{\mathbf{BIL}}\) and we will prove that these extensions are sound and complete with respect to a certain classes of basic frames. Finally, we prove that the logic BIL+ and some of its extensions are complete respect with the class of neighborhood frames.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2024.06.24;
  2023.11.22
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;2;
  53
• Subject:
  interpretability logic;
  Kripke frames;
  neighbourhood frames;
  Veltman semantics
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/52596 ;
  2449-836X;
  10.18778/0138-0680.2023.26
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  image