 From this it follows that \(*\) must be monotonic in the sense that if \(K \subseteq K'\) then \(K*p \subseteq K'*p\), since if \(q \in K*p\) then \((p&gt;q) \in K\) by (RT) so \(K \subseteq K'\) gives \((p&gt;q) \in K'\) and hence by (RT) again \(q \in K'*p\). But this is a conclusion which goes against intuition, and unless the allowed belief sets \(K\) are severely limited, contradicts ostensibly reasonable assumptions about \(*\), including in particular that if \(p\) is consistent with \(K\) then \(K*p\) should be simply the logical consequences of \(K \cup\{p\}\).