A single proof of classical behaviour in da Costa’s \(C_n\) systems
Published in Electronic Notes in Theoretical Computer Science, 2015
A strong negation in da Costa’s systems can be naturally extended from the strong negation \(\neg\) of \(C_1\). In [Newton C. A. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4):497–510, 10 1974] Newton da Costa proved the connectives \(\{\rightarrow, \land, \lor, \neg\}\) in \(C_1\) satisfy all schemas and inference rules of classical logic. In the following paper we present a proof that all logics in the \(C_n\) herarchy also behave classically as \(C_1\). This result tell us the existance of a common property among the paraconsistent family of logics created by da Costa.
Recommended citation: M. Osorio and J. Castellanos Joo, “A single proof of classical behaviour in da Costa’s Cn systems”, Electronic Notes in Theoretical Computer Science, vol. 315, pp. 3–16, Sep. 2015, ISSN: 1571-0661. DOI: 10.1016/j.entcs.2015.06.002
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