Semantical considerations on nonmonotonic logic
Artificial Intelligence
Possible-world semantics for autoepistemic logic
Readings in nonmonotonic reasoning
On the relation between default and autoepistemic logic
Artificial Intelligence
All I know: a study in autoepistemic logic
Artificial Intelligence
Negation by default and unstratifiable logic programs
Selected papers of the workshop on Deductive database theory
Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
Relating autoepistemic and default logics
Proceedings of the first international conference on Principles of knowledge representation and reasoning
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Translating default logic into standard autoepistemic logic
Journal of the ACM (JACM)
Fixpoint 3-valued semantics for autoepistemic logic
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Nonmonotonic Logic II: Nonmonotonic Modal Theories
Journal of the ACM (JACM)
Introduction to Default Logic
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Fixpoint semantics for logic programming a survey
Theoretical Computer Science
Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning about Knowledge
Introduction: progress in formal commonsense reasoning
Artificial Intelligence - Special issue on logical formalizations and commonsense reasoning
Ultimate approximation and its application in nonmonotonic knowledge representation systems
Information and Computation
Any-world assumptions in logic programming
Theoretical Computer Science
Epistemic foundation of stable model semantics
Theory and Practice of Logic Programming
Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
ACM Transactions on Computational Logic (TOCL)
Well-founded and stable semantics of logic programs with aggregates
Theory and Practice of Logic Programming
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic Programming
Fundamenta Informaticae
Predicate Introduction for Logics with Fixpoint Semantics. Part II: Autoepistemic Logic
Fundamenta Informaticae
Rough Sets and Approximation Schemes
RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
Approximation Schemes in Logic and Artificial Intelligence
Transactions on Rough Sets IX
Towards an axiom system for default logic
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Only-knowing: taking it beyond autoepistemic reasoning
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Well-founded semantics and the algebraic theory of non-monotone inductive definitions
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Embedding nonground logic programs into autoepistemic logic for knowledge-base combination
ACM Transactions on Computational Logic (TOCL)
On the intertranslatability of argumentation semantics
Journal of Artificial Intelligence Research
An algebraic account of modularity in ID-logic
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
Default reasoning with preference within only knowing logic
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
Representation of partial knowledge and query answering in locally complete databases
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Nonmonotonic logics and their algebraic foundations
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Predicate introduction under stable and well-founded semantics
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
Correct Reasoning
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic Programming
Fundamenta Informaticae
Predicate Introduction for Logics with Fixpoint Semantics. Part II: Autoepistemic Logic
Fundamenta Informaticae
Approximating operators and semantics for abstract dialectical frameworks
Artificial Intelligence
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We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise one-to-one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.