Semantical considerations on nonmonotonic logic
Artificial Intelligence
Logic programs with classical negation
Logic programming
Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Cumulative default logic: in defense of nonmonotonic inference rules
Artificial Intelligence
Well founded semantics for logic programs with explicit negation
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
The complexity of default reasoning under the stationary fixed point semantics
Information and Computation
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
On Finding Extensions of Default Theories
ICDT '92 Proceedings of the 4th International Conference on Database Theory
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Well-founded semantics for extended logic programs with dynamic preferences
Journal of Artificial Intelligence Research
The complexity of propositional default logics
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
Fundamenta Informaticae
Computation of Extensions of Seminormal Default Theories
Fundamenta Informaticae
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Default logic is one of the most popular approaches to model defeasible reasoning. Nevertheless, there are a number of problems with Reiter's original semantics that have led to the investigation of alternative approaches. In particular, Baral/Subrahmanian and Przymusinska/Przymusinski have investigated generalizations of well-founded semantics for normal logic programs to default logic. These generalizations have a number of interesting properties. Unfortunately, it turns out that in many realistic situations they are unable to draw any defeasible conclusions at all - which can hardly be viewed as satisfactory. We show how this difficulty can be solved by varying the fixed point operator underlying the semantics. We define a range of different semantics. All of them are correct wrt. safe conclusions under Reiter semantics, i.e. those conclusions with the same proof in all extensions. For the strongest semantics we have also completeness in the case of coherent default theories, i.e. default theories with at least one extension. The logics differ in the effort spent for determining potential conclusions. It turns out that they are at least as complex as original default logic. We show that our approach also leads to new semantics for normal and extended logic programs. Moreover, we define prioritized versions of the logics.