Semantical considerations on nonmonotonic logic
Artificial Intelligence
Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
A theory of diagnosis from first principles
Artificial Intelligence
A logical framework for default reasoning
Artificial Intelligence
Reasoning about priorities in default logic
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Expressing preferences in default logic
Artificial Intelligence
A Deductive System for Non-Monotonic Reasoning
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Smodels - An Implementation of the Stable Model and Well-Founded Semantics for Normal LP
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
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Consistency-based approaches in nonmonotonic reasoning may be expected to yield multiple sets of default conclusions for a given default theory. Reasoning about such extensions is carried out at the meta-level. In this paper, we show how such reasoning may be carried out at the object level for a large class of default theories. Essentially we show how one can translate a (normal) default theory Δ, obtaining a second Δ′, such that Δ′ has a single extension that encodes every extension of Δ. Moreover, our translated theory is only a constant factor larger than the original (with the exception of unique names axioms). We prove that our translation behaves correctly. In the approach we can now encode the notion of extension from within the framework of standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension. This result has some theoretical interest, in that it shows how multiple extensions of normal default theories are encodable with manageable overhead in a single extension.