# Non-Monotonic Reasoning

From International Center for Computational Logic

# Non-Monotonic Reasoning

Entailment in classical logics (e.g. first-order predicate logic) is

*montone*, that is, if a formula F follows from a set S of formulas, then F also follows from any superset of S.Non-monotonic reasoning is concerned with entailment relations that do not satisfy monotonicity. Such relations can be used to model default assumptions (such as “delivery is free of charge unless stated otherwise”), rules with exceptions (e.g. “birds typically fly, but penguins do not fly”) or priorities between rules (e.g. federal law trumping state law).

The research area investigates the formal modelling of various approaches to non-monotonic reasoning, analyses and compares such entailment relations and also deals with implementations and applications, e.g. in knowledge representation, logic programming, legal reasoning, or Natural-Language Understanding.