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Intellektik: Technical report 92-24

Considerations on Default Logics

Torsten Schaub

The ability to reason seems to be one of the distinguishing marks of intelligent behavior. However, the available underlying information is quite often incomplete. As a result, conclusions frequently have to be drawn in the absence of information. A formal approach to reasoning in the absence of information, or to reason by default, is given by default logic --- a logical system developed by Raymond Reiter. The approach taken by default logic is extensively studied and further developed in this thesis. After surveying various approaches to default reasoning, we thoroughly investigate Reiter's original approach in order to identify its properties and limitations.

The major contributions of this thesis are threefold. First, an alternative approach to default logic is developed in order to address the limitations of the original approach and subsequent variants. The resulting system is called constrained default logic. The approach has clear semantical foundations and remedies the problems encountered in the original approach in an arguably simpler way than other proposals. Second, we provide differing semantical characterizations for several default logics. In particular, we develop a uniform semantical framework for default logics in terms of Kripke structures. This approach provides a simple but meaningful instrument for comparing existing default logics in a unified setting. Third, we examine in detail the relationships among the variations of default logic. As a result, we obtain several criteria for the coincidence of the examined approaches. Moreover, we provide a general approach for incorporating nonmonotonic lemmas into default logics.

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