An überconsistent logic is one where the set of logical truths is inconsistent. Examples of such logics have been known for a long time. However, it has recently been recognized that this is an important new class of logics. Dialetheism is the view that some contradictions are true. Since logical truths are true, it might be thought that these logics provide an important new argument for dialetheism. However, matters are not that straightforward. This paper is an initial discussion of the matter. The first part of the paper provides the background on paraconsistency and dialetheism required for the discussion. The second half is a discussion of three überconsistent logics and their bearing on dialetheism. The first is the logic LP with a logical constant for the value both true and false; the second is Second-Order LP; the third is a certain kind of connexive logic.
Graham Priest (Fri,) studied this question.