 If &lt;W, R&gt; is a Chellas frame, a triple &lt;W, R, P&gt; is said to be a Segerberg frame (or a general frame) for CCL if P is a binary relation on ℘(W) that satisfies certain closure conditions. A quintuple M = &lt;W, R, P, v+, v−&gt; then is a general model for CCL if &lt;W, R, P&gt; is a general frame for CCL, &lt;W, R, v+, v−&gt; is a model for CCL, and for every propositional variable p, [[p]],[[~p]] ∈ P. The closure conditions on P are exactly the conditions guaranteeing that for every formula A, [[A]],[[~A]] ∈ P if for every propositional variable p, [[p]],[[~p]] ∈ P. If [[A]],[[~A]] is seen as the proposition expressed by A, then a general model for CCL is rich enough to guarantee that every proposition expressed by a formula is available. This is needed for a purely structural correspondence theory. The formula A □→ A, for example, is valid on a general frame iff it satisfies the frame condition: