Journal of Logic Programming
A logical framework for default reasoning
Artificial Intelligence
An algorithm to compute circumscription
Artificial Intelligence
A circumscriptive theorem prover
Artificial Intelligence
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
Nonmonotonic reasoning: logical foundations of common sense
Nonmonotonic reasoning: logical foundations of common sense
Beginnings of a theory of general database completions
ICDT '90 Proceedings of the third international conference on database theory on Database theory
Default theories of Poole-type and a method for constructing cumulative versions of default logic
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
General patterns in nonmonotonic reasoning
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Generalized Bottom-Up Query Evaluation
EDBT '92 Proceedings of the 3rd International Conference on Extending Database Technology: Advances in Database Technology
Specifying Closed World Assumptions for Logic Databases
MFDBS '89 Proceedings of the 2nd Symposium on Mathematical Fundamentals of Database Systems
Deduction with Supernormal Defaults
Proceedings of the Second International Workshop on Nonmonotonic and Inductive Logic
On Indefinite Databases and the Closed World Assumption
Proceedings of the 6th Conference on Automated Deduction
Possible Worlds Semantics for Credulous and Contraction Inference
KI '01 Proceedings of the Joint German/Austrian Conference on AI: Advances in Artificial Intelligence
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
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Our aim is to clarify which nonmonotonic consequence relation λ Δ it given by a set Δ of "supernormal" defaults, i.e. defaults of the form (true : δ)/δ There are in fact a number of proposals for λ Δ (e.g. the skeptical and the credulous semantics). In this paper we look at the space of all possible default semantics and try to characterize the known ones by their properties, especially the valid deduction rules. For instance, it seems reasonable to require that any useful semantics should coincide with the original CWA if this is consistent. We might also want to allow proofs by case analysis. Then we get the skeptical semantics (assuming some other very natural deduction rules). Our results are in fact completeness proofs for "natural deduction systems" based on different default semantics.