On the Mutual Definability of the Notions of Entailment, Rejection, and Inconsistency
نویسنده
چکیده
In this paper, two axiomatic theories T ́ and T1 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 T1 it is replaced by the notion of the family Incons of inconsistent sets. The author has proved that the theories T+, T ́, and T1 are equivalent.
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عنوان ژورنال:
- Axioms
دوره 5 شماره
صفحات -
تاریخ انتشار 2016