When declaiming a line of reasoning, it is the custom to present a case for the object of discourse. During the argument, the propositions are steadily built up, monotonically increasing. But, in non-monotonic logic, the propositions are defeasible; that is, if an impasse is reached, the propositions can be abandoned; thus the number of valid propositions no longer has to increase steadily, but can even decrease and further fluctuate.

This form of reasoning can thus be used to model thought, as in the scientific method, where hypothetical explanations can be abandoned in the light of further evidence from observation, inference, and experiment.

Formal logics of this type include Default Logic, Circumscription, and Autoepistemic logic.