The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
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Artificial Intelligence
On the problem of computing the well-founded semantics
Theory and Practice of Logic Programming
Ultimate approximation and its application in nonmonotonic knowledge representation systems
Information and Computation
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
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AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
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LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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ESWC 2009 Heraklion Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications
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PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
ICLP '09 Proceedings of the 25th International Conference on Logic Programming
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LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
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Theory and Practice of Logic Programming
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
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SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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Annals of Mathematics and Artificial Intelligence
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Journal of Artificial Intelligence Research
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Journal of Artificial Intelligence Research
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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Approximation theory is a fixpoint theory of general (monotone and non-monotone) operators which generalizes all main semantics of logic programming, default logic and autoepistemic logic. In this paper, we study inductive constructions using operators and show their confluence to the well-founded fixpoint of the operator. This result is one argument for the thesis that Approximation theory is the fixpoint theory of certain generalised forms of (non-monotone) induction. We also use the result to derive a new, more intuitive definition of the wellfounded semantics of logic programs and the semantics of ID-logic, which moreover is easier to implement in model generators.