Raymond Reiter came up with the idea of "default logic" in 1980, a nonmonotonic way to formalise reasoning with default assumptions.

Standard logic can only say that something is true or false. Default logic, on the other hand, can say things like "by default, something is true." It is a problem because a lot of reasoning is based on facts that are true most of the time but only sometimes. "Birds usually fly" is a well-known example. Standard logic says that this rule can be stated either as "all birds fly," which is wrong because penguins don't fly or as "all birds that aren't penguins and aren't ostriches and...", which needs to list all the exceptions to the rule. The goal of default logic is to formalise rules of inference like this one without making all of their exceptions clear.

Overview

When a smart system (whether a computer or a person) tries to solve a problem, it may have all the information it needs, and its main job is to use classical reasoning to come to the correct conclusions. In these situations, simple predicate logic might be enough. But there are many times when the system needs to have all the information it needs. For example, it could be because some information is unavailable or because it needs to act quickly and needs more time to get all the information it needs. 

Classical logic can represent and make sense of some parts of information that aren't complete. However, when there is a knowledge gap, it is necessary to "fill in" the gaps by making educated guesses. When this happens, the system must make some sense guesses. In the case of default reasoning, these guesses are based on rules of thumb called defaults. For example, a physician in an emergency room must guess the most probable reasons for the symptoms.

Restrictions

A default is definite or has no prerequisites if it doesn't have any (or, equivalently, its prerequisite is tautological). A default is normal if it only has one reason for being the way it is, which is the same as its conclusion. Default is both categorical and normal if it is both. Default is normal if all of its reasons lead to the same conclusion. If all of the defaults in a default theory are categorical, normal, supernormal, or seminormal, then the theory is said to be categorical, normal, supernormal, or seminormal.

Conclusion

Important things that must be in place for successful application development in these areas are:

1) An understanding of the basic ideas, and 

2) Powerful ways to put those ideas into action.

Default logic is a meaningful way to represent and reason about knowledge because it lets you reason with incomplete information and because defaults are standard in many application domains, such as diagnostic problems, information retrieval, legal reasoning, rules, system and software specifications, etc. Default logic can be used to model reasoning with incomplete information, which was its original purpose, or as a way to represent information compactly. 

Furthermore, the operational interpretations make it easy for learners to apply ideas to real-world problems. It is essential because you should know how hard it is to understand Default Logic. Students at the University of Toronto were asked to rate the difficulty of several nonmonotonic reasoning formalisms. Default Logic, based on fixpoints, was ranked as the second hardest, after the full version of Circumscription but well ahead of Autoepistemic Logic.