In　this　paper,　we　firstly　introduce　a　concept　of　inconsistency　classification　based　on　which　we　draw　a　qualitative　conclusion　that　the　approach　by　Hu　and　Gercone　for　computing　an　attribute　core　based　on　Skowron＇s　discernibility　matrix　is　correct　for　both　consistent　and　partially　inconsistent　decision　tables,　but　may　fail　to　work　for　entirely　inconsistent　ones.　Secondly,　we　improve　the　work　of　Zhi　and　Miao　concerning　the　computation　of　core　attributes　by　defining　a　new　binary　discernibility　matrix.　Finally,　as　another　application　of　inconsistency　classification,　we　show　that　an　attribute　core　from　the　algebra　view　is　equivalent　to　that　from　the　information　view　not　only　for　consistent　but　also　for　partially　inconsistent　decision　tables.