A Proof Theory for Constructive Default Logic

We present what we call Constructive Default Logic (CDL) a default logic in which the fixedpoint definition of extensions is replaced by a constructive definition which yield so-called constructive extensions. Selection functions are used to represent explicitly the control of the reasoning process in this default logic. It is well-known that Reiter's original default logic lacks, in general, a default proof theory. We will show that CDL does have a default proof theory, and we will also show that this is related to the fact that CDL has the existence property for constructive extensions and that it also has the semi-monotonicity property. Furthermore, we will also show that, with respect to some counter-examples that were suggested by Lukaszewicz, constructive extensions yield more intuitive conclusions than Reiter’s extensions. Hence, constructive default logic does not only have heuristic advantages over Reiter’s default theory from a computational point of view, but it is also more adequate with respect to knowledge representation. 1 This research was partly supported by the ESPRIT III BRA Project 6156 DRUMS 2.