Default Reasoning

Researchers in artificial intelligence have developed the formal study of argumentation as defeasible reasoning in a logical, computational, and epistemological perspective.

1. Default reasoning

From the logical point of view, defeasible reasoning is studied within non-monotonic logic. Unlike conventional (“monotonic”) logic, non-monotonic logic admits the possibility that a conclusion can be deductible from a set of premises {P1} and not from {P1} plus new premises. In terms of belief, the challenge is to formalize the basic idea that the provision of new information may lead to revision of the belief derived from a formerly limited set of data.

From an epistemological perspective, the theory of defeasible reasoning (Koons 2005) concerns beliefs that permit exceptions: in general, birds fly; but penguins (Sphenisciformes, Spheniscidae) are birds and do not fly. As a consequence, if the only thing one knows about Tweety is that Tweety is a bird, it is not possible, strictly speaking, to infer that Tweety can or cannot fly. Nonetheless, in the absence of any information suggesting that Tweety is a penguin (or some other flightless bird), the theory of revisable reasoning admits the conclusion “Tweety flies”. It validates exception-conditioned inferences:

Since A (Tweety is a bird), normally B (Tweety flies).

The premise does support the conclusion, but it may nonetheless be true and the conclusion false. A conclusion considered to be correct on the basis of the knowledge which has now become available, may later turn out to be false if further knowledge is gained.

The theory of defeasible reasoning also addresses more complex issues such as the following. We know that:

(1) Birds fly
(2) Tweety is a bird
(3) Tweety does not fly
(4) Birds have highly developed wings muscles

In these conditions, can we deduce (5) from (1) – (4)?

(5) Tweety has highly developed wings muscles

The property of having highly developed wing muscles is linked to having the capacity to fly, which, according to the available information (3), is not true in Tweety’s case. The inference from (1) and (4) to (5) is therefore invalidated. In other words, the conclusion “Tweety has highly developed wings muscles” is deducible not from “Tweety is a bird” but from “Tweety is a flying bird”.

A conclusion C asserted through defeasible reasoning can be rebutted in two ways:
— On the one hand, upon the existence of good arguments for a conclusion inconsistent with C (“rebutting defeater”, Koons 2005), that is to say upon the existence of a strong counter-argumentation.
— On the other hand, upon the existence of good reasons to think that the transition principles usually invoked in the argument do not apply in the case considered (“undercutting defeaters”, ibid), S. Refutation.

2. Representation of default reasoning

The default inference is represented as a default rule:

If Tweety is a bird,
in the absence of information suggesting that Tweety may be a penguin (etc.),
it is legitimate to conclude that Tweety flies.

The sequence is represented as:

Tweety is a bird: Tweety is not a penguin (etc.)

Tweety flies
ζ : η


ζ: Prerequisite: we know that ζ
η: justification: η is compatible with available information
θ: conclusion

The historical origins of the theory of revisable reasoning are sought in dialectical reasoning and the Topics of Aristotle. The restriction “in the absence of information” corresponds exactly to the “modal” component of Toulmin’s layout of argument; the basic intuitions and concepts are the same. Toulmin layout can be schematized as:

D (Data) : R (Rebuttal)

C (Claim)

D, Data: Prerequisites, we know that D.
R, Justification: The inference from D to C could be rebutted under the conditions R1… Rn; but we have no information leading us to believe that these rebuttal conditions are actually true.
C, Claim: So, the conclusion C can be accepted; one can work on the basis that C.

Gabbay & Woods (2003) develops a study of practical reasoning combining the insights of and relevance theory and default reasoning theory.