Nonmonotonic

Nonmonotonic refers to properties of systems in which adding information can invalidate previous conclusions or inhibit the inference of further conclusions. In contrast, monotone systems preserve entailment: once something is inferred, it remains entailed as more premises are added.

In logic and artificial intelligence, nonmonotonic logic studies formalisms that model default reasoning and revisable beliefs. These systems allow conclusions to be withdrawn in light of new information. Classic examples include default logic (Reiter), circumscription, and autoepistemic logic. A common illustrative pattern is the default assumption that typically, birds fly, which is retracted when learning that a particular bird is a penguin. Such frameworks aim to capture everyday reasoning more closely than classical, monotonic logics.

In mathematics and computer science, monotonicity also describes functions that preserve order (if x ≤ y then f(x) ≤ f(y)). Nonmonotonic functions fail to preserve order and may increase or decrease irregularly. In programming and algorithms, nonmonotonic behavior refers to processes whose results depend on the sequence or timing of inputs, and where additional data can change earlier outputs.

In linguistics and semantics, nonmonotonicity arises in the interpretation of context, implicatures, and presuppositions, where conclusions can be canceled or revised as discourse information evolves.

See also: Monotonic logic, Default logic, Circumscription, Autoepistemic logic, Belief revision.