Conservative extension concepts for nonmonotonic knowledge bases

Conservative extensions of logical theories play an important role in software engineering. They provide a formal basis for program refinement and guarantee the integrity and transparency of modules and objects. This paper provides a detailed analysis of conservative extension concepts in the context of nonmonotonic knowledge bases, in particular default theories. Since there are different approaches to nonmonotonic reasoning based on different strategies for dealing with multiple extensions, we define several alternative refinement concepts and study their interrelationships. We also show that refinement is well behaved with respect to strong stratification, a technique for reducing computational effort in default reasoning.