Deduction Theorem - Paraconsistent Deduction Theorem

Paraconsistent Deduction Theorem

In general, the classical deduction theorem doesn't hold in paraconsistent logic. However, the following "two-way deduction theorem" does hold in one form of paraconsistent logic:

if and only if ( and )

that requires the contrapositive inference to hold in addition to the requirement of the classical deduction theorem.