 One useful approach to updating is to assign time indices to the sentences, as proposed by Katsuno and Mendelzon (1992). Then the belief set will not consist of sentences \(p\) but of pairs \(\langle p,t_1\rangle\) of a sentence \(p\) and a point in time \(t_1\), signifying that \(p\) holds at \(t_1\). In the book-and-magazine example, let \(t_1\) denote the point in time that the first statement refers to, and \(t_2\) the moment when the second information was given in Case 2. The original belief set contained the pair \(\langle \neg(p\leftrightarrow q),t_1\rangle\). (\(\neg(p\leftrightarrow q)\) is the exclusive disjunction of \(p\) and \(q\).) Revision by \(p\) can be represented by the incorporation of \(\langle p,t_1\rangle\), and updating by \(p\) by the incorporation of \(\langle p,t_2\rangle\) into the belief set. It follows quite naturally that \(\langle \neg q,t_1\rangle\) is implied by the revised belief set but not by the updated belief set.