 As mentioned earlier in this subsection, the assumption that agents’ possibility sets partition the state space depends on the modeler’s choice of specific axioms for the knowledge operators. For example, if we drop axiom K5 (preserving the validity of K1–K4) the agent’s possibility sets need not partition the space set (follow the link for an  example.  For more details and applications, cf. Samet 1990.) It was conjectured (cf. Geanakoplos 1989) that lack of negative introspection (i.e. systems without K5) would allow to incorporate unforeseen contingencies in the epistemic model, by representing the agents’ unawareness of certain events (i.e. the case in which the agent does not know that an event occurs and also does not know that she does not know that.) It was later shown by Dekel et al. (1998) that standard models are not suitable to represent agents’ unawareness. An original non-standard model to represent unawareness is provided in Heifetz et al. (2006). For a comprehensive bibliography on modeling unawareness and applications of the notion, cf. the external links at the end on this entry.