Paraconsistency: The Logical Way to the Inconsistent by Walter A. Carnielli (Repost)

Description

A logic is paraconsistent if it can be used as the underlying logic for inconsistent but nontrivial theories, called paraconsistent theories. A theory is explosive if the addition to it of any contradiction is sufficient to make it trivial. Paraconsistent logics are not, in general, explosive. In paraconsistent logics the scope of the principle of (non-)contradiction is, in a certain sense, restricted. We may even say, as da Costa does, that if the strength of this principle is restricted in a system of logic, then the system belongs to the class of paraconsistent logics.