Description

• Title:
  A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB
• Creator:
  Inoue, Takao
• Contributor:
  Meiji Pharmaceutical University, Department of Medical Molecular Informatics, Tokyo, Japan; Hosei University, Graduate School of Science and Engineering Tokyo, Japan;
  takaoapple@gmail.com
• Description:
  In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as(M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)\),(M2) \(I^M(\neg \phi) = \neg I^M(\phi)\),(M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b .\wedge . \Diamond p_b \supset p_a\),where \(p_a\) and \(p_b\) are propositional variables corresponding to the name variables \(a\) and \(b\), respectively. In the last, we shall give some comments including some open problems and my conjectures.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2022.03.10;
  2021.11.09
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;4;
  50
• Subject:
  Le´sniewski’s ontology;
  propositional ontology;
  translation;
  interpretation;
  modal logic;
  KTB;
  soundness;
  Grzegorczyk’s modal logic
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/41066 ;
  2449-836X;
  10.18778/0138-0680.2021.25
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other