When a set of rules generates (conflicting) values for a virtual attribute of some tuple, the system must resolve the inconsistency and decide on a unique value that is assigned to that attribute. In most current systems, the conflict is resolved based on criteria that choose one of the rules in the conflicting set and use the value that it generated. There are several applications, however, where inconsistencies of the above form arise, whose semantics demand a different form of resolution. We propose a general framework for the study of the conflict resolution problem, and suggest a variety of resolution criteria, which collectively subsume all previously known solutions. With several new criteria being introduced, the semantics of several applications are captured more accurately than in the past. We discuss how conflict resolution criteria can be specified at the schema or the rule-module level. Finally, we suggest some implementation techniques based on rule indexing, which allow conflicts to be resolved efficiently at compile time, so that at run time only a single rule is processed.