The use of inference rules to draw conclusions from a knowledge base relies implicitly on a general property of some logics (including propositional and FOL) called monotonicity. A logic is monotonic if when we add some new rules to a knowledge base, then all the original sentences of this knowledge base still follow from the larger one. In non-monotonic reasoning, the set of beliefs does not grow monotonically over time. This means that when new knowledge is gained, some previous conclusions may be retracted.
To create deterministic rules covering all patterns in a data base, the data sets describing the objects must be perfect and contain all necessary information. In addition, we will need examples of all objects having unique features. Only then will it be possible to create deterministic rules for all possible situations, covering also so far unseen objects. Even if it is possible to create deterministic rules, these rules may be too specific and not usable for so far unseen objects. Therefore we are also interested in patterns, described by the rules, which not necessarily are correct in all cases, but in most.
Very often, we do not have exact information about all aspects of an object, nor perfectly describing rules. What we would like is some kind of default information, telling us how the world usually is. This could be given as a rule which for instance says that birds usually can fly, and unless we are given more information about a specific bird, we will believe that the bird flies. Such a rule would be a default rule.
Reiter has formalized the concept of default rules in the so called Default Logic of Reiter, see [Rei80]. By using a non-monotonic reasoning strategy, conclusions are drawn from defaults. These defaults are kept consistent with the intended model. This way of reasoning seems to be useful in explanation finding.
A framework called Poole's Theorist[PGA86, Poo88, Poo89] has been created based on the default logic of Reiter. This framework regards defaults as possible hypotheses to be used in a theory to explain the answers. A uniform deductive reasoning mechanism is used to construct explanations of observations in terms of facts and hypotheses.
Theorist distinguishes facts from defaults, and uses deduction to construct consistent theories explaining the observations. The theorist knowledge base is a collection of formulas, with each of these being either a possible hypothesis (), a fact () or observation(G).
In Chapter 
, and algorithm is described which
creates a variant of default rules based on these principles.