Abstract: Since its introduction in 1977, abstract interpretation has inspired a lot of research and is now widely applied in program analyses and verification fields. Therefore, a universe model was constructed for existing studies on abstract interpretation, which unifies and is equivalent to all the current frameworks of abstract interpretation. Based on this, several fundamental problems were raised about abstract interpretation that need to be solved. This model and the relevant problems can be viewed as the basic points for further development of abstract interpretation theory.

Key words: abstract interpretation, semantics, universe domain, completeness