Making inconsistency respectable: a logical framework for inconsistency in reasoning

We claim there is a fundamental diierence between the way humans handle inconsistency and the way it is currently handled in formal logical systems: To a human, resolving inconsistencies is not necessarily done by \restoring" consistency but by supplying rules telling one how to act when the inconsistency arises. For artiicial intelligence there is an urgent need to revise the view that inconsistency is a \bad" thing, and instead view it as mostly a \good" thing. Inconsistencies can be read as signals to take external action, such as \ask the user", or invoke a \truth maintenance system", or as signals for internal actions that activate some rules and deactivate other rules. There is a need to develop a framework in which inconsistency can be viewed according to context, as a vital trigger for actions, for learning, and as an important source of direction in argumentation. Unfortunately the consensus of opinion in the logic community is that inconsistency is undesirable. Many believe that databases should be completely free of inconsistency, and try to eradicate inconsistency from databases by any means possible. Others address inconsistency by isolating ir, and perhaps resolving it locally. All seem to agree, however, that data of the form q and :q, for any proposition q cannot exist together, an that the connict must be resolved somehow. This view is too simplistic for capturing common-sense reasoning, and furthermore , fails to use the beneets of inconsistency in modelling cognition. In-consistecy in information is the norm, and we should feel happy to be able 1