Natural deduction for paraconsistent logic (Q2746598)

The authors define a hierachy of natural deduction systems \(\text{NDC}_n\), \(1\leq n\leq \omega\) and show that, for each \(n\), \(\text{NDC}_n\) is equivalent to the da Costa paraconsistent logic \(C_n.\) Most axioms are replaced by the obvious corresponding rules but reductio and excluded middle, interestingly, are replaced by rules distributing negation over disjunction and implication. A direct proof, involving simple valuations, of soundness and completeness is given for each \(\text{NDC}_n.\)