 After presenting this problem, Voorbraak (1993) proposed to deal with it by discarding the bridge principle \(K\varphi \rightarrow {B\varphi}\). Another option is to allow inconsistent beliefs (Gochet &amp; Gribomont 2006: Section 2.6). Still, a further possible solution, closer to the spirit of these notes, is to consider an intermediate notion of ’knowledge’ that is not as strong as the absolute irrevisable (i.e., irrevocable) notion given by the S5 modal operator K. More precisely, the proposal in Baltag and Smets (2008) looks at Lehrer’s defeasibility theory of knowledge (Lehrer 1990; Lehrer &amp; Paxson 1969), and works with the indefeasible (“weak”, non-negatively-introspective) knowledge given, in the  plausibility models  discussed above, by the modality \([\leq]\) (read before also as safe belief). Indeed, Lehrer and Stalnaker call this concept defeasible knowledge, a form of knowledge that might be defeated by false evidence, but cannot be defeated by true evidence. The concept satisfies both the truth axiom \(([\leq]\varphi \rightarrow \varphi)\) and positive introspection \(([\leq]\varphi \rightarrow [\leq][\leq]\varphi)\), but it lacks negative introspection; thus, the previous derivation of inconsistent beliefs from an agent mistakenly believing that she (defeasibly) knows \(\varphi\) \(({B[\leq]\varphi} \land \lnot [\leq]\varphi)\) is no longer possible. Instead, it can be easily shown how a belief in defeasible knowledge, \({B[\leq]\varphi}\), is equivalent to a simple belief, \({B\varphi}\).