Computing Extensions of Default Theories

We have presented a theoretical characterisation of sets of defaults generating an extension of a default theory: complete and regular universes. We have then defined the concept of valid exclusion, and have given with the help of that concept another characterisation of complete and regular universes. This last result allows us an encoding of a default theory into a set of clauses involving typed literals. Resolution followed by some deletion algorithms then computes every extension of the default theory. Contrary to previously published papers, this method works for any propositional default theory.