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Axioms 2016, 5(2), 15; doi:10.3390/axioms5020015

On the Mutual Definability of the Notions of Entailment, Rejection, and Inconsistency

Department of Philosophy, Cardinal Stefan Wyszyński University in Warsaw, Wóycickiego 1/3, 01-938 Warsaw, Poland
Academic Editor: Humberto Bustince
Received: 25 February 2016 / Revised: 23 May 2016 / Accepted: 25 May 2016 / Published: 7 June 2016
(This article belongs to the Special Issue Lvov—Warsaw School)
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Abstract

In this paper, two axiomatic theories T and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T it is replaced by the notion of Słupecki’s rejection consequence Cn and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent sets. The author has proved that the theories T+, T, and T′ are equivalent. View Full-Text
Keywords: deductive system; entailment; rejection; inconsistency; Tarski’s consequence theories; rejection theory; inconsistency theory; equivalence of theories deductive system; entailment; rejection; inconsistency; Tarski’s consequence theories; rejection theory; inconsistency theory; equivalence of theories
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wybraniec-Skardowska, U. On the Mutual Definability of the Notions of Entailment, Rejection, and Inconsistency. Axioms 2016, 5, 15.

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