Description

• Title:
  Literal and Controllable Paraconsistency
• Creator:
  Ciuciura, Janusz
• Description:
  The principle of explosion asserts that any formula can be derived from any pair of other contradictory formulas. Paraconsistent logic is typically regarded as a logic in which the universal validity of this principle is questioned. Therefore, a key point is determining when the validity can be considered universal to classify a logic as paraconsistent. A pertinent example to illustrate this point is the calculus CB1 that admits the principle but only for negated formulas, i.e., from any set {α, ∼α} any other formula follows if and only if α is of the form ∼γ. Another example is Sette’s calculus P1, which is paraconsistent at the level of variables but not complex formulas. Both serve as compelling examples of the so-called borderline cases. In this paper, we examine several calculi expected to be paraconsistent at the level of literals. It means that a pair of formulas, α and ∼α, can yield any β if, and only if α is neither a propositional variable nor is its iterated negation. Furthermore, it is assumed that in some calculi presented here, β must adhere to specific restrictions. Once these conditions are satisfied, we refer to calculus as paraconsistent in a “controllable manner”.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Janusz Ciuciura
• Date:
  2024.11.02
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Online First Articles; 1-19;
  Logic and Logical Philosophy; Prace online; 1-19;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/46686/40255
• Subject:
  paraconsistent logic;
  Sette’s calculus;
  paraconsistency;
  paranormal logics
• Identifier: https://apcz.umk.pl/LLP/article/view/46686
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text