Logic programs with ordered disjunction

Logic programs with ordered disjunction (LPODs) contain a new connective which allows representing alternative, ranked options for problem solutions in the heads of rules: A x B intuitively means that if possible A, but if A is not possible, then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show how LPODs can be implemented using answer set solvers for normal programs. The implementation is based on a generator, which produces candidate answer sets and a tester which checks whether a given candidate is maximally preferred and produces a better candidate if it is not. We also discuss the complexity of reasoning tasks based on LPODs and possible applications.