%0 Article %A Grant John %D 1995 %G English %B Acta cybernetica %@ 0324-721X %T The optimistic and cautious semantics for inconsistent knowledge bases %U http://acta.bibl.u-szeged.hu/12541/1/cybernetica_012_numb_001_037-055.pdf %X We develop two alternative semantics, based on maximal consistent subsets, for knowledge bases that (possibly) contain inconsistencies. The optimistic (resp. cautious) semantics correspond to entailment in some (resp. all) maximal consistent subsets. We develop a Kripke-style model theory corresponding to these two semantics. We further extend these semantics to the case when knowledge bases contain both explicit and nonmonotonic negation. Notions of stratification and stability are defined and studied for both semantics.