 In Kraus, Lehmann, and Magidor (1990), rules ID\(_{\pipsim}\), LLE\(_{\pipsim}\), RW\(_{\pipsim}\), CCut\(_{\pipsim}\) and CMon\(_{\pipsim}\) together define the system C of cumulative reasoning; AND\(_{\pipsim}\) is a derived rule of C. If OR\(_{\pipsim}\) is added, one gets system P of preferential reasoning; if one keeps AND\(_{\pipsim}\), CCut\(_{\pipsim}\) can be derived from the other rules of P.