Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
Logic programs with classical negation
Logic programming
Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Artificial intelligence and mathematical theory of computation
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
A Terminological Interpretation of (Abductive) Logic Programming
LPNMR '95 Proceedings of the Third International Conference on Logic Programming and Nonmonotonic Reasoning
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)
Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates
Proceedings of the 17th International Conference on Logic Programming
Extending Classical Logic with Inductive Definitions
CL '00 Proceedings of the First International Conference on Computational Logic
A Deductive System for FO(ID) Based on Least Fixpoint Logic
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
An approximative inference method for solving ∃¬so satisfiability problems
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
Satisfiability checking for PC(ID)
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Annals of Mathematics and Artificial Intelligence
Connecting first-order ASP and the logic FO(ID) through reducts
Correct Reasoning
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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Existing formalisations of (transfinite) inductive definitions in constructive mathematics are reviewed and strong correspondences with LP under least model and perfect model semantics become apparent. I point to fundamental restrictions of these existing formalisations and argue that the well-founded semantics (wfs) overcomes these problems and hence, provides a superior formalisation of the principle of inductive definition. The contribution of this study for LP is that it (re-) introduces the knowledge theoretic interpretation of LP as a logic for representing definitional knowledge. I point to fundamental differences between this knowledge theoretic interpretation of LP and the more commonly known interpretations of LP as default theories or autoepistemic theories. The relevance is that differences in knowledge theoretic interpretation have strong impact on knowledge representation methodology and on extensions of the LP formalism, for example for representing uncertainty.