Making inconsistency respectable: A logical framework for inconsistency in reasoning, part I — A position paper

Abstract

We claim there is a fundamental difference 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 artificial 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.