Non-monotonic logic

A relation of inference is ‘monotonic’ if the addition of premises does not undermine previously reached conclusions; otherwise the relation is non-monotonic. Deductive inference, at least according to the canons of classical logic, is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premises are added.

By contrast, everyday reasoning is mostly non-monotonic because it involves risk: we jump to conclusions from deductively insufficient premises. We know when it is worthwhile or even necessary (for example, in medical diagnosis) to take the risk. Yet we are also aware that such inference is ‘defeasible’ – that new information may undermine old conclusions. Various kinds of defeasible but remarkably successful inference have traditionally captured the attention of philosophers (theories of induction, Peirce’s theory of abduction, inference to the best explanation, and so on). More recently logicians have begun to approach the phenomenon from a formal point of view. The result is a large body of theories at the interface of philosophy, logic and artificial intelligence.