Reasoning about preferences is a major issue in many decision making problems. Recently, a new logic for handling preferences, called Qualitative Choice Logic (QCL), was presented. This logic adds to classical propositional logic a new connective, called ordered disjunction symbolized by . That new connective is used to express preferences between alternatives. QCL was not designed to handle conditional preferences, even if it is possible to express an implication with a preference on the left hand side, for instance "(Air France Virgin) Hotel Package".
We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based on the notion of projection; then we study restrictions over the representations of the knowledge base and of the query, and find new polynomial classes of abduction problems.