Monotonicity in Rule Based Update

An important characteristic for many formulations of knowledge representation and reasoning is that they are nonmonotonic. It has been, however, illustrated that under certain conditions, a formulation may satisfy some restricted monotonicity in its reasoning [2]. In this paper, we investigate this issue under the context of rule based update. We first present a general framework of rule based update in which a knowledge base is viewed as a set of literals and can be updated with a set of update rules which is represented by an extended logic program (also called update program). We then show that given a knowledge base B and an update program \Pi, (1) there exist some facts that can be always added into B such that updating the expansion of B with \Pi will not destroy any fact obtained from the update of B with \Pi, and (2) on the other hand, there also exist some update rules that can be always added into \Pi such that updating B with the expansion of \Pi will not destroy any fact ob..