Tableau systems for logics of formal inconsistency - Carnielli, Walter A.; Marcos, João (Proceedings of the International Conference on Artificial Intelligence (IC-AI'2001), 2001)
The logics of formal inconsistency (LFIs) are logics that allow to explicitly formalize the concepts of consistency and inconsistency by means of formulas of their language. Contradictoriness, on the other hand, can always be expressed in any logic, provided its language includes a symbol for negation. Besides being able to represent the distinction between contradiction and inconsistency, LFIs are non-explosive logics, in the sense that a contradiction does not entail arbitrary statements, but yet are gently explosive, in the sense that, adjoining the additional requirement of consistency, then contradictoriness do cause explosion. Several logics can be seen as LFIs, among them the great majority of paraconsistent systems developed under the Brazilian and Polish tradition. We present here tableau systems for some important LFIs: bC, Ci and LFI1.