Description

• Title:
  Some results on Jaśkowski’s discursive logic
• Creator:
  de Moraes, Lafayette;
  Abe, Jair Minoro
• Description:
  Jaśkowski [3] presented a new propositional calculus labeled “discussive propositional calculus”, to serve as an underlying basis for inconsistent but non-trivial theories. This system was later extended to lower and higher order predicate calculus ([1], [2]). Jaśkowski’s system of discussive or discursive propositional calculus can actually be extended to predicate calculus in at least two ways. We have the intention using this calculus of building later as a basis for a discussive theory of sets. One way is that studied by Da Costa and Dubikajtis. Another one is developed in this paper as a solution to a problem formulated by Da Costa. In this work we study a first order discussive predicate calculus J∗∗ .The paper consists of three parts. In the first part we introduce the calculus J∗∗ and, following Prof. D. Makinson’s suggestion, we show that it is not identical with the predicate calculus [2] of Da Costa and Dubikajtis. An axiomatization of J∗∗ is presented. In the second one, we introduce new discussive connectives and study some of the properties. We observe that the usual Kripke semantics can be adapted to the calculus J∗∗ .
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Date:
  2004.01.19
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; No. 9 (2001); 25-33;
  Logic and Logical Philosophy; Nr 9 (2001); 25-33;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2001.002/2695
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2001.002
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text