Semantical considerations on nonmonotonic logic
Artificial Intelligence
On the relation between default and autoepistemic logic
Artificial Intelligence
All I know: a study in autoepistemic logic
Artificial Intelligence
Quantification in autoepistemic logic
Fundamenta Informaticae - Special issue: logics for artificial intelligence
Minimal belief and negation as failure
Artificial Intelligence
Levesque's axiomatization of only knowing is incomplete
Artificial Intelligence
Definability and commonsense reasoning
Artificial Intelligence
The logic of knowledge bases
Revisiting quantification in autoepistemic logic
ACM Transactions on Computational Logic (TOCL)
Uniform semantic treatment of default and autoepistemic logics
Artificial Intelligence
A Sequent Calculus for Skeptical Default Logic
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Epistemic semantics for fixed-points non-monotonic logics
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
Only-knowing: taking it beyond autoepistemic reasoning
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Reasoning about Conditions and Exceptions to Laws in Regulatory Conformance Checking
DEON '08 Proceedings of the 9th international conference on Deontic Logic in Computer Science
Rule Calculus: Semantics, Axioms and Applications
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
A Semantical Account of Progression in the Presence of Defaults
Conceptual Modeling: Foundations and Applications
A semantical account of progression in the presence of defaults
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A semantic characterization of a useful fragment of the situation calculus with knowledge
Artificial Intelligence
Confluent Term Rewriting for Only-knowing Logics
Proceedings of the 2010 conference on STAIRS 2010: Proceedings of the Fifth Starting AI Researchers' Symposium
Correct Reasoning
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Recently, Lakemeyer and Levesque proposed a logic of only-knowing which precisely captures three forms of nonmonotonic reasoning: Moore's Autoepistemic Logic, Konolige's variant based on moderately grounded expansions, and Reiter's default logic. Defaults have a uniform representation under all three interpretations in the new logic. Moreover, the logic itself is monotonic, that is, nonmonotonic reasoning is cast in terms of validity in the classical sense. While Lakemeyer and Levesque gave a model-theoretic account of their logic, a proof-theoretic characterization remained open. This paper fills that gap for the propositional subset: a sound and complete axiom system in the new logic for all three varieties of default reasoning. We also present formal derivations for some examples of default reasoning. Finally we present evidence that it is unlikely that a complete axiom system exists in the first-order case, even when restricted to the simplest forms of default reasoning.