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- Title
On the Mutual Definability of the Notions of Entailment, Rejection, and Inconsistency.
- Authors
Wybraniec-Skardowska, Urszula
- 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.
- Subjects
DEFINABILITY theory (Mathematical logic); ENTAILMENT (Logic); INCONSISTENCY (Logic); AXIOMATIC set theory; MATHEMATICAL equivalence
- Publication
Axioms (2075-1680), 2016, Vol 5, Issue 2, p15
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms5020015