Reasoning with contradictory information using quasi-classical logic

The proof theory of quasi-classical logic (QC logic) allows the derivation of non-trivializable classical inferences from inconsistent information. A non-trivializable, or paraconsistent, logic is, by necessity, a compromise, or weakening, of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in a classical manner. Here we motivate the need for QC logic, present a proof theory, and semantics for the logic, and compare it to other paraconsistent logics.