The problem of logical omniscience is often presented as having originated from within the subject known as epistemic logic. In this setting, knowledge is treated as a modal operator \(K_i\) where sentences of the form \(K_i \phi\) are assigned the intended interpretation agent \(i\) knows that \(\phi\). The goal is to then set down axioms and rules which characterize how we should reason about statements of this form. For instance the principle that knowledge of a statement entails its truth is rendered as \(K_i \phi \rightarrow \phi\) and the principle that knowledge of a conjunction entails knowledge of its conjuncts is rendered as \(K_i(\phi \wedge \psi) \rightarrow (K_i \phi \wedge K_i \psi)\). Other principles – e.g. \(\neg K_i \phi \rightarrow K_i \neg K_i \phi\), which expresses that \(i\)’s failure to know \(\phi\) entails that he knows of this failure – are considered more controversial. However the consensus view (e.g., Hintikka 1962; Lenzen 1978; Fagin et al. 1995) is that the most defensible choices of logics of knowledge lie between the modal systems \(\textsf{S4}\) and \(\textsf{S5}\).