 Sets of possibilities represent states of knowledge. In the example, \(\{ \bar{p} \bar{q} \bar{r}, p \bar{q} \bar{r}, \bar{p} q \bar{r}, \bar{p} \bar{q} r, pq \bar{r}, p \bar{q} r, \bar{p} qr, pqr \}\) represents the state of complete ignorance about propositions \(p, q, r\). Singleton sets like \(\{ pq \bar{r} \}\) represent states of full knowledge about these propositions, and the empty set \(\varnothing\) represents the inconsistent state that results from processing incompatible statements about \(p, q\) and \(r\). Here we spell out the dynamic meanings of the statements of our propositional language: 