 Propositional logic (the logic of negation, disjunction and conjunction) can be viewed as an update logic as follows. Consider the case where we have three basic propositions \(p, q\) and \(r\), and we know nothing about their truth. Then there are eight possibilities: \(\{ \bar{p} \bar{q} \bar{r}, p \bar{q} \bar{r}, \bar{p} q \bar{r}, \bar{p} \bar{q} r, pq \bar{r}, p \bar{q} r, \bar{p} qr, pqr \}\) Here \(\bar{p} \bar{q} \bar{r}\) should be read as: none of \(p, q, r\) is true, \(p \bar{q} \bar{r}\) as: \(p\) is true but \(q\) and \(r\) are false, and so on. If now \(\neg p\) (“not \(p\)”) is announced, four of these disappear, and we are left with \(\{\bar{p} \bar{q} \bar{r}, \bar{p} q \bar{r}, \bar{p} \bar{q} r, \bar{p} qr\}\). If next \(q \vee \neg r\) (“\(q\) or not \(r\)”) is announced, the possibility \(\bar{p} \bar{q} r\) gets ruled out, and we are left with \(\{ \bar{p} \bar{q} \bar{r}, \bar{p} q \bar{r}, \bar{p} qr \}\). And so on. We can view the meaning of propositions like \(\neg p\) and \(q \vee \neg r\) as mappings from sets of possibilities to subsets thereof.