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 that is not deducible from a set of premises {P1} can be deduced from {P1} augmented of additional 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 allow for exceptions: in general, birds fly; but penguins (Sphenisciformes, Spheniscidae) are birds and do not fly. Consequently, 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. Nevertheless, in the absence of any information suggesting that Tweety is a penguin (or some other flightless bird), the theory of revisable inference permits 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 we have now , may turn out to be false later, when further knowledge is gained.
The theory of defeasible reasoning also addresses complex questions 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 wing 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 related to having the ability to fly, which, according to the available information (3), is not true in the case of Tweety. The inferences 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 refuted in two ways:
— On the one hand, by 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 transitional principles usually invoked in the argument do not apply in the case considered (“undercutting defeaters”, ibid), S. Refutation.
2. Representation of default reasoning
The reasoning (1) is represented as (2
(1) If Tweety is a bird,
in the absence of information suggesting that Tweety might be a penguin (etc.),
it is legitimate to conclude that Tweety flies.
(2)
| Tweety is a bird: Tweety is not a penguin (etc.) — Tweety flies |
ζ : η — θ |
ζ: Prerequisite: we know that ζ
η: Rationale: η is compatible with available information
θ: Conclusion
The historical origins of the theory of revisable reasoning are to be 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; we can assume that C.
Gabbay & Woods (2003) develop a study of practical reasoning that combine the insights of relevance theory and default reasoning theory.