 This modality has the properties of an S4 modal operator; hence, it is factive, positively introspective but not negatively introspective. In Baltag and Smets (2008), it is argued that this modality is well suited to express a version of Lehrer’s indefeasible (“weak”, non-negatively-introspective) type of knowledge (Lehrer 1990; Lehrer &amp; Paxson 1969), and the authors explain how it can be understood as belief that is persistent under revision with any true piece of information. Using this modality (also read as safe belief in Baltag &amp; Smets 2008), it is possible to define syntactically a notion of simple belief as truth in the most plausible worlds: 