Non-Monotonic Logic

Non-monotonic logic is a family of formal systems designed to model reasoning in which conclusions can be retracted when new information becomes available. Unlike classical logic, where adding premises never invalidates previous derivations, non-monotonic systems capture the defeasible character of everyday and scientific inference: a conclusion held as probable or default-true may be abandoned when defeating evidence emerges.

The formal significance of non-monotonic logic is that it attempts to reconstruct defeasible reasoning within a rigorous framework. Systems such as default logic, autoepistemic logic, and circumscription provide proof-theoretic or model-theoretic accounts of how an agent should revise its belief set when its information state changes. The field connects artificial intelligence — where robots and expert systems must reason under uncertainty — with philosophy of science, where the logic of theory revision has been studied since Popper and Kuhn.

The central difficulty is tractability. Non-monotonic inference is computationally harder than classical inference because the set of possible belief revisions grows exponentially with the number of potential defeaters. This has led to hybrid approaches that combine non-monotonic reasoning with probabilistic methods, treating defeasible inference as approximate inference in a Bayesian network rather than as discrete belief revision.