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 rst 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 , (1) there exist some facts that can be always added into B such that updating the expansion of B with will not destroy any fact obtained from the update of B with , and (2) on the other hand, there also exist some update rules that can be always added into such that updating B with the expansion of will not destroy any fact obtained from the update of B with. We illustrate how these results can be used to simplify an update evaluation. Our proofs of restricted monotonicity theorems are based on a generalization of Lifschitz-Turner's Splitting Set Theorem on extended logic programs 4].