A tutorial on Nonmonotonic Reasoning

Abstract

Nonmonotonic reasoning, in its broadest sense, is reasoning to conclusions on the basis of incomplete information. Given more information, we are prepared to retract previously drawn inferences. To exhibit the classic example: if all we know about Tweety is that he is bird, then we plausibly conclude that he can fly; on learning that Tweety is a penguin, we withdraw that conclusion. We call this reasoning nonmonotonic because the set of plausible conclusions does not grow monotonically with increasing information.

As Tweety shows, commonsense reasoning has a nonmonotonic component, and it has been argued that almost all commonsense inferences are of this sort. The attempt to formalize nonmonotonic reasoning so that computer programs could use it as part of their reasoning repertoire was begun by John McCarthy in the 1970's, and the early 1980's saw the development of the major nonmonotonic families: circumscription, default logic, and modal nonmonotonic logics. At the same time, proof methods that were clearly nonmonotonic were also being developed: the so-called Truth Maintenance Systems, and negation-as-failure in logic programming and deductive databases.

From the end of the 1980's to the present there has been an explosion in research in nonmonotonic reasoning. We now understand much better the properties of the major formalisms from a metatheoretic point of view, the relationships among the formalisms, and their connection to independently-developed proof methods. The goal of this monograph is to make this understanding more accessible. For those outside the area, the quantity and technical depth of the material can be a formidable barrier to understanding and applying nonmonotonic methods. For those actively pursuing research, it is often useful to have a concise guide to the major formalisms and their interrelationships. We intend this monograph to serve both purposes. We have tried to present the formalisms as simply and concisely as possible, stressing the connections among them and unresolved issues for future research.