On Notions of Completeness Weaker than Kripke Completeness

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. 1 Motivation It is known that Kripke frames correspond to complete, atomic and completely additive Boolean algebras with operators (baos). This fact became the basis of duality theory for Kripke frames, developed in the 1970's by Thomason [13], Goldblatt [4] and others. In this paper, we are going to investigate notions of completeness and consequence weaker than those associated with standard Kripke frames from an algebraic perspective. Our starti...

• Type: Conference
• Year: 2004
• Where: AIML
• Authors: Tadeusz Litak
• Keywords: AIML 2004, AIML 2008, Completeness Properties, Kripke Completeness, Kripke Frames