 Just like the corresponding operations for belief sets, revision operations for belief bases can be constructed out of two suboperations: expansion by \(p\) and contraction by \(\neg p\). According to the Levi identity, \((A* p = (A\div \neg p) +' p)\), the contractive suboperation should take place first. Alternatively, the two suboperations may take place in reverse order, \(A* p = (A+'p) \div \neg p\). This latter possibility does not exist for belief sets. If \(K\cup \{p\}\) is inconsistent, then \(K+p\) is always the same, namely identical to the whole language, independently of the identity of \(K\) and of \(p\), so that all distinctions are lost. For belief bases, this limitation is not present, and thus there are two distinct ways to obtain revision from contraction and expansion: