Nonmonotonic Integrity Constraints

Abstract. Semantics of multidimensional dynamic logic programming is traditionally based on the causal rejection principle: if there is a conflict between rules then the rule from a less preferred program is rejected. However, sometimes it is useful to solve a conflict between the heads of rules by blocking the body of a rule. Moreover, semantics based on the causal rejection principle, is not able to recognize conflicts, which are not manifested as conflicts between the heads of rules. Nonmonotonic integrity constraints are discussed in this paper. They provide alternative solutions of conflicts (as compared with solutions based on causal rejection principle). Conceptual apparatus introduced in this paper enables also to distinguish more preferred interpretations and, consequently, it is relevant for logic programming with preferences. Nonmonotonic integrity constraints and other notions introduced in the paper (falsified assumptions, more preferred assumptions) contribute to bridging the gap between research in fields as belief revision or preference handling on the one hand and multidimensional dynamic logic programming on the other hand