A local approach to reasoning under inconsistency in stratified knowledge bases

This paper investigates an approach for reasoning under inconsistency in a "local" way, in prioritized knowledge bases. In such bases, the higher the layer, the more certain, the more reliable are the formulas stored in this layer. The proposed approach is based on the notion of (consistent) argument whose strength depends on the layer of the least certain formulas involved in the argument. Each formula in the base is also associated with a "level of paraconsisten cy" which reflect to what extent there exists arguments that support both a formula and its negation. Three consequence relations are presented and compared. Two of them aim at maximizing the certainty degree and/or at minimizing the level of para- consistency of the conclusion. The third one produces consequences that are safely supported in the sense that there exists an undefeated argument for them (whose certainty is greater than its paraconsistency).