Defeasibility in Reasoning and Nonmonotonic Inference

Though defeasibility also applies to reactive agents, it acquires its fullest meaning in cognitive agents: defeasible cognition consists in achieving certain cognitive states (beliefs, intentions, etc.) when provided with certain normal cognitive inputs (perceptions, beliefs, intentions), but refraining adopting these states when the normal inputs are accompanied by further elements. More specifically, the idea takes on a more precise content when referred to reasoning, i.e., to inference or argumentation. A defeasible reasoning process (an inference or argument pattern) responds to typical input premises with certain default conclusions, but fails to deliver those conclusions when the typical input premises are accompanied by further premises, indicating exceptional circumstances.
The most cited example of a default inference concerns Tweety the penguin. Let us assume that we are told that Tweety is a bird, and that we know that birds usually fly. Given this information we would normally conclude that Tweety flies. Assume, however, that we are later told that Tweety is a penguin, and that also know that while also penguins are birds, they not fly. Given all this information, while continuing to believe that Tweety is a bird and that birds usually fly, we should refrain from endorsing the conclusion that Tweety flies. In fact, we now know that he is a special kind of bird, namely, a penguin, to which the default rule does not apply.
As this example shows, the addition of premises in a defeasible reasoning may lead to the withdrawal of a conclusion. This aspect of defeasible reasoning is conceptualised through the distinction between monotonic and nonmonotonic reasoning. In general, we say that an inference method is monotonic when it behaves as follows: any conclusion that can be obtained from an initial set of premises can still be obtained whenever the original set is expanded with additional premises. More precisely, all conclusions that are derived through monotonic inferences from a premise set \(S_{1}\) can also be derived from any larger (more inclusive) premises set \(S_{2}\) (\(S_{1}\subseteq S_{2})\).
Correspondingly, an inference method is nonmonotonic when it behaves as follows: a conclusion that can be obtained from an initial set of premises may no longer be obtainable when the original set is expanded with additional premises. More precisely, conclusions that are derived through nonmonotonic inferences from a premise set \(S_{1}\) may no longer be derivable from a larger (more inclusive) set of premises \(S_{2}\).
Deduction is monotonic: as long as we accept all premises of a deductive inference, we must continue to accept its conclusion. Therefore, we also say that deductive inference is conclusive : as long as we maintain the premises, any additional information will not affect the conclusion.
By contrast, defeasible inferences are nonmonotonic: we may reject the conclusion of a defeasible inference while maintaining all of its premises. This may indeed happen when further premises are provided that substantiate exceptions to the defeasible inference. In defeasible reasoning “ if the premises hold, the conclusion also holds tentatively, in the absence of information to the contrary” (Walton 2008 160). Thus, defeasible inference
relies on absence of information as well as its presence, often mediated by rules of the general form: given P , conclude Q unless there is information to the contrary. (Horty 2001, 337).
Defeasible reasoning is not only a matter of practice but also one of rational justification, as stated in the following definition:
Reasoning is defeasible  when the corresponding argument is rationally compelling but not deductively valid. The truth of the premises of a good defeasible argument provide support for the conclusion, even though it is possible for the premises to be true and the conclusion false. In other words, the relationship of support between premises and conclusion is a tentative one, potentially defeated by additional information. (Koon 2009).
As we shall see in what follows, in many situations we are entitled or justified to derive default conclusions and to maintain those conclusions until we come to appreciate that circumstances obtain under which such conclusions should not be retained