On Notions of Completeness Weaker than Kripke Completeness.
Tadeusz Litak · Advances in Modal Logic · 2004
We are going to show that the standard notion of Kripke completeness is the strongest one among many provably distinct algebraically motivated completeness properties, some of which seem to be of intrinsic interest. More specifically, we are going to investigate notions of completeness with respect to algebras which are either atomic, complete, completely additive or admit residuals (the last notion of completeness coincides with conservativity of minimal tense extensions); we will be also interested in combinations of these properties.