 In the 1965 paper “Semantical Analysis of Modal Logic II”, Kripke extends the model theory to treat non-normal modal systems, including Lewis’s S2 and S3. Though these systems are considered somewhat unnatural, their model theory is deemed elegant. Completeness and decidability results are proved vis-à-vis the proper class of structures, including the completeness of S2 and S3, and the decidability of S3. To achieve these results, the model theory is extended by the introduction of non-normal worlds which do not respect the standard Leibnizian interpretation of \(\Box\) as truth in every accessible world, and that make every formula of the form \(\Box B\) false. This leads to a corresponding revision of the interpretation of \(\Box\), and to the introduction of a new element \(N\subseteq K\) in the model structures \((G, K, R, N). N\) is the subset of normal worlds which respect the standard interpretation of \(\Box\). Non-normal worlds are needed to prevent the validity of formulas like \(\Box\Box A\) even when \(\Box A\) is valid, by basically allowing A but not \(\Box A\) to be true in every world accessible from the actual world and thus \(\Box A\) but not \(\Box\Box A\) to hold in the actual world. This is required as the systems under consideration do not have a full rule of necessitation. Another interesting aspect of the non-normal systems is that in the model theoretic results that pertain to them, \(G\) (the actual world) plays an essential role, in particular in the S2 and S3 model structures the actual world has to be normal. Instead, the full rule of necessitation that holds in normal systems eliminates the need of non-normal worlds and makes the choice of \(G\) model theoretically irrelevant.