Disjunctive Abduction

Given an observation or a goal, abduction infers candidate hypotheses to explain the observation or to achieve the goal. In this paper, we consider disjunctive abduction, in which disjunctions play important roles in abduction. Machine-oriented intelligent systems can utilize disjunctive abduction in many ways. For example, consider the case in which multiple explanations exist for an observation. We may need to select the best explanation among them, but often it is difficult to choose only one given insufficient information. In that case, we can leave the decision indefinite by considering a disjunctive explanation, which is a disjunction of possible alternative explanations. Disjunctive explanations can offer a consistent way to theory changes when they 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. A 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 well applicable to view updates in disjunctive databases. We also show that disjunctive abduction can be considered in inductive logic programming.