Description

• Title:
  On axiomatization of Łukasiewicz's four-valued modal logic
• Creator:
  Tkaczyk, Marcin
• Description:
  Formal aspects of various ways of description of Jan Łukasiewicz’s four-valued modal logic £ are discussed. The original Łukasiewicz’s description by means of the accepted and rejected theorems, together with the four-valued matrix, is presented. Then the improved E.J. Lemmon’s description based upon three specific axioms, together with the relational semantics, is presented as well. It is proved that Lemmon’s axiomatic is not independent: one axiom is derivable on the base of the remanent two. Several axiomatizations, based on three, two or one single axiom are provided and discussed, including S. Kripke’s axiomatics. It is claimed that (a) all substitutions of classical theorems, (b) the rule of modus ponens, (c) the definition of “◊” and (d) the single specific axiom schema: ⬜A ∧ B → A ∧ ⬜B, called the jumping necessity axiom, constitute an elegant axiomatics of the system £.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Date:
  2011.11.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 20 No. 3 (2011); 215-232;
  Logic and Logical Philosophy; Tom 20 Nr 3 (2011); 215-232;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2011.012/803
• Subject:
  Łukasiewicz’s modal logic;
  axiomatization;
  modal logic
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2011.012
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text