The Anomalous Extension Problem in Default Reasoning

Abstract In their recent celebrated paper, Hanks and McDermott presented a simple problem in temporal reasoning which showed that a seemingly natural representation of a frame axiom in nonmonotonic logic can give rise to an anomalous extension, i.e., one which is counter-intuitive in that it does not appear to be supported by the known facts. An alternative, less formal approach to nonmonotonic reasoning uses the mechanism of a truth maintenance system (TMS). Surprisingly, when reformulated in terms of a TMS, the anomalous extension noted by Hanks and McDermott disappears. We analyze the reasons for this. First it is seen that anomalous extensions are not limited to temporal reasoning, but can occur in simple nontemporal default reasoning as well. In these cases also, the natural TMS representation avoids the problem. Exploring further, it is observed that the form of the TMS justifications resembles that of nonnormal default rules. Nonnormal rules have already been proposed as a means of avoiding anomalous extensions in some nontemporal reasoning situations. It appears that, suitably formulated, they can exclude the anomalous extension in the Hanks-McDermott case also, although the representation does not adjust smoothly to fresh information, as does the TMS. Some variant of default logic appears to be required to provide a correct semantic basis for truth maintenance systems.