Signed systems for paraconsistent reasoning

We present a novel approach to paraconsistent reasoning, that is, to reasoning from inconsistent information. The basic idea is the following. We transform an inconsistent theory into a consistent one by renaming all literals occurring in the theory, Then, we restore some of the original contents of the theory by introducing progressively formal equivalences linking the original literals to their renamings. This is done as long as consistency is preserved. The restoration of the original contents of the theory is done by appeal to default logic. The overall approach provides us with a family of paraconsistent consequence relations. Our approach is semantical because it works at the level of the propositions; it deals with the semantical link between a proposition and its negation. The approach is therefore independent of the combination of the connectives that are actually applied to the propositions in order to form entire formulas.