  Recall the example of Alice, Bob and the Ford from Section 2.1.1. Let \(W=\{a, b, c\}\) corresponding to the worlds in which Alice owns the Ford, Bob own the Ford and no one in the office owns the Ford.  Suppose the probability function \[\Pr(a) =\frac{6}{10}, \Pr(b)=\frac{3}{10} \text{ and } \Pr(c)=\frac{1}{10}\] captures my partial beliefs. For Lockean thresholds in the interval \((.75,.9]\), my full beliefs are exhausted by \(\Bel=\{ \{a,b\}, W\}.\) Now suppose I were to learn that Alice does not own the Ford. That is consistent with all beliefs in \(\Bel\), but since \(\Pr(\{a,b\} | \{b,c\}) = \frac{3}{4}\) it follows by the Lockean thesis that \(\{a,b\} \notin \Bel_{\{b,c\}}\). So Lockeanism does not in general validate Preservation. The good news, at least for those sympathetic to Pollock’s critique of non-monotonic logic, is that the Lockean thesis allows for undercutting defeat of previous beliefs.