The Idea of Defeasibility in Logic and AI

Logic and artificial intelligence have played a key role in providing a precise analysis of these notions (see Ginzberg 1997 for a collection of seminal contributions on nonmonotonic reasoning, Horty 2001 and Koon 2009 for a discussion of nonmonotonic logics, and Blair 2012, Ch. 9, on defeasibility in the context of argumentation theories).
Pollock (2010) observes that Chisholm (1957) was the first epistemologist to use the term defeasible , taking it from Hart (1951). Among the philosophers who have addressed aspects of defeasibility is Stephen Toulmin whose approach to reasoning is based on the idea that inference rules or warrants connect data and conclusions of arguments. In the following passage he claims that some of these warrants are defeasible:
Warrants are of different kinds, and may confer different degrees of force on the conclusions they justify. Some warrants authorise us to accept a claim unequivocally, given the appropriate data […]; others authorise us to make the step from data to conclusion either tentatively, or else subject to conditions, exceptions, or qualifications (Toulmin 1958, 100).
According to Toulmin, defeasibility has a special place in the law:
Again, it is often necessary in the law-courts, not just to appeal to a given statute or common-law doctrine, but to discuss explicitly the extent to which this particular law fits the case under consideration, whether it must inevitably be applied in this particular case, or whether special facts may make the case an exception to the rule or one in which the law can be applied only subject to certain qualifications (Toulmin 1958, 101).
Defeasibility is also addressed by Nicholas Rescher, who deals with it in connection dialectics (Rescher 1977) and presumptive reasoning (Rescher 2006). Rescher (1977, 6) describes defaults as “provisoed assertions”, having the logical form P/Q and meaning that:
P generally (or usually or ordinarily) obtains provided that Q ” or “P obtains, other things being equal, when Q does” or “when Q , so ceteris paribus does P ” or “P obtains in all (or most) ordinary circumstances (or possible worlds) when Q does” or “Q constitutes prima facie evidence for P .”
The assertion of P under proviso Q , combined with the assertion of Q , constitutes and argument for P , though Q does not “entail, imply or ensure P”, but makes Q only “normal, natural, and only to be expected” (Rescher 1977, 7).
The most influential and comprehensive model of defeasibility is the one provided by John Pollock, who as noted introduced the ideas of undercutting and rebutting, as well as the technique of labelling defeasible inference graphs to determine their justification status (see Pollock 1995, 2010).
Particularly influential in contemporary research on informal logic has been the account of defeasible reasoning provided by Doug Walton. According to Walton (1996, 42-43)
presumptive reasoning is neither deductive nor inductive in nature, but represents a third distinct type of reasoning of the kind classified by Rescher (1976) as plausible reasoning, an inherently tentative kind of reasoning subject to defeat by special circumstances (not defined inductively or statistically) or a particular case. (pp. 42–43)
Walton, Reed, and Macagno (2008) identify a number of distinct argumentation patterns, called argument schemes, each of which can be challenged by appropriate critical questions acting as pointers to possible defeaters.
In artificial intelligence and logic, some formal approaches have been developed to capture the normality assumption embedded in defeasible reasoning: things are assumed be normal unless we have evidence to the contrary. This assumption can be modelled by minimising the extension of predicates that express abnormality conditions (McCarthy 1980). A similar idea underlies negation by failure, used in logic programming: atomic propositions are assumed to be false unless they can be shown to be true (Clark 1978). Preferential defeasible logics (see Kraus, Lehmann, and Magidor 1990) are based on the idea that the defeasible implications of a set of premises are those propositions that are true in the most normal models (situations) that satisfy those formulas.
The idea of defeasible reasoning as the application of default inference rules supporting non-deductive presumptive inferences has been developed by Reiter (1980). An elegant and broadly scoped model of reasoning with defaults, meant to capture the link between reasons and the conclusions they favour, has recently been proposed by Horty (2007, 2012).
A large amount of AI research has been recently developed which merges defeasible reasoning and argumentation (Rahwan and Simari 2009). In particular, the abstract account of argumentation proposed by Dung (1985) has been very influential. Its abstractness lies in the fact that it focuses on attack (defeat) relations between arguments rather than on these arguments’ internal structure.