Nonmonotonic Logic pp 37-103 | Cite as

# General default theories

## Abstract

In this chapter we introduce default logic. Default logic is concerned with proof systems which are obtained from propositional logic by adding some nonstandard inference rules called *defaults*. A default differs from an inference rule, as defined in the previous chapter, in that its premises are of two types. Premises of the first type, called *prerequisites*, act in the same way as the premises of an inference rule. In order to apply a default it is necessary that each of its prerequisites be proved. Premises of the second type, called *justifications*, do not need a proof. It is only required that each of them be *possible* in order for a default to be applicable. In this chapter we will formally define defaults and default logic and make precise what is meant by a proof and by being possible. To this end, we will introduce the notion of an *extension* for a default theory. Extensions can be thought of as descriptions of all possible knowledge (belief) sets that are represented by a default theory. They play a similar role to that of the set of all consequences of a theory in propositional logic. In this chapter we study the notion of an extension and provide several characterizations of extensions as well as algorithms to compute them.

## Keywords

Inference Rule Consequence Operator Proof System Default Rule Default Theory## Preview

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