Full Idea
Epistemic accessibility should be required to be reflexive (allowing Kφ→φ). S4 allows the 'KK principle', or 'positive introspection' (Kφ→KKφ), and S5 allows 'negative introspection' (¬Kφ→K¬Kφ).
Clarification
KK is knowing that you know (or that you don't know)
Gist of Idea
Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K)
Source
Theodore Sider (Logic for Philosophy [2010], 7.2)
Book Reference
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.185