Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and 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)
A procedural semantics for well-founded negation in logic programs
Journal of Logic Programming
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Default theories that always have extensions
Artificial Intelligence
Graph theoretical structures in logic programs and default theories
Theoretical Computer Science
Foundations of logic programming
Principles of knowledge representation
Stable models and non-determinism in logic programs with negation
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Alternative foundations for Reiter's default logic
Artificial Intelligence
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
Extending and implementing the stable model semantics
Artificial Intelligence
Resolution for Skeptical Stable Model Semantics
Journal of Automated Reasoning
On the equivalence and range of applicability of graph-based representations of logic programs
Information Processing Letters
WFS + Branch and Bound = Stable Models
IEEE Transactions on Knowledge and Data Engineering
NoMoRe: Non-monotonic Reasoning with Logic Programs
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Sequent Calculi for Default and Autoepistemic Logics
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
A Sequent Calculus for Skeptical Default Logic
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Graphs and colorings for answer set programming with preferences
Fundamenta Informaticae
Transformation-based bottom-up computation of the well-founded model
Theory and Practice of Logic Programming
On the problem of computing the well-founded semantics
Theory and Practice of Logic Programming
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
Normal forms for answer sets programming
Theory and Practice of Logic Programming
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
The Diagnosis Frontend of the dlv system
AI Communications
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Graph theoretical characterization and computation of answer sets
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Justifications for logic programs under answer set semantics
Theory and Practice of Logic Programming
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
Tableau calculi for answer set programming
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
Tableau Calculi for Logic Programs under Answer Set Semantics
ACM Transactions on Computational Logic (TOCL)
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We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We start with different characterizations of answer sets in terms of totally colored dependency graphs that differ in graph-theoretical aspects. We then develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. In this way, we obtain an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Furthermore, we distinguish operations corresponding to Fitting's operator as well as to well-founded semantics.