Given some evidence or observation, abduction infers candidate hypotheses to explain such an observation. In this paper, we consider the case in which multiple explanations exist but we cannot select one from them. Our approach leaves the decision indefinite, but offers a consistent way to theory changes. A disjunctive explanation, which is a disjunction of possible alternative explanations, is introduced for this purpose. For abduction, such a disjunction is useful when obtained explanations are incorporated or assimilated into the current knowledge base. The assimilated knowledge base preserves the intended semantics from the collection of all possible updated knowledge bases. The merit of disjunctive explanations is that we only need one current knowledge base at a time, still keeping every possible change in a single state. This method is extended to accomplish an update when there are multiple ways to remove old unnecessary hypotheses from the knowledge base. The proposed framework is also well applied to view updates in disjunctive databases. Finally, disjunctive explanations are considered in induction, where we take the disjunction of multiple rules. In this case, disjunctive explanations correspond to take the greatest specialization of rules under implication.