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