Description

• Title:
  Twist-Valued Models for Three-Valued Paraconsistent Set Theory
• Creator:
  Carnielli, Walter A.;
  Coniglio, Marcelo E.
• Description:
  We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our framework is adapted to provide a class of twist-valued models generalizing Löwe and Tarafder’s model based on logic (PS 3,∗), showing that they are paraconsistent models of ZFC. The present approach offers more options for investigating independence results in paraconsistent set theory.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Logic and Logical Philosophy
• Date:
  2021.05.04
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 30 No. 2 (2021): June; 187-226;
  Logic and Logical Philosophy; Tom 30 Nr 2 (2021): Czerwiec; 187-226;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2020.015/26269
• Subject:
  Paraconsistent set theory;
  Boolean-valued models;
  axiomatic set theory;
  twist structures;
  logics of formal inconsistency;
  three-valued paraconsistent logics;
  Leibniz’s Law;
  03E40;
  03E70
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2020.015
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text