Journal of Logic Programming
Possible-world semantics for autoepistemic logic
Readings in nonmonotonic reasoning
On the relation between default and autoepistemic logic
Artificial Intelligence
Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
Bilattices and the semantics of logic programming
Journal of Logic Programming
Journal of the ACM (JACM)
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
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
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Contributions to the Theory of Logic Programming
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
Fixpoint semantics for logic programming a survey
Theoretical Computer Science
Uniform semantic treatment of default and autoepistemic logics
Artificial Intelligence
Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates
Proceedings of the 17th International Conference on Logic Programming
Well-founded and stable semantics of logic programs with aggregates
Theory and Practice of Logic Programming
Logic programs with monotone abstract constraint atoms*
Theory and Practice of Logic Programming
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
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
Well-founded semantics for description logic programs in the semantic web
ACM Transactions on Computational Logic (TOCL)
Nonmonotonic logics and their algebraic foundations
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Well-Supported semantics for logic programs with generalized rules
Correct Reasoning
Abstract dialectical frameworks revisited
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Approximating operators and semantics for abstract dialectical frameworks
Artificial Intelligence
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In this paper we study fixpoints of operators on lattices and bilattices in a systematic and principled way. The key concept is that of an approximating operator, a monotone operator on the product bilattice, which gives approximate information on the original operator in an intuitive and well-defined way. With any given approximating operator our theory associates several different types of fixpoints, including the Kripke-Kleene fixpoint, stable fixpoints, and the well-founded fixpoint, and relates them to fixpoints of operator being approximated. Compared to our earlier work on approximation theory, the contribution of this paper is that we provide an alternative, more intuitive, and better motivated construction of the well-founded and stable fixpoints. In addition, we study the space of approximating operators by means of a precision ordering and show that each lattice operator O has a unique most precise-we call it ultimale-approximation. We demonstrate that fixpoints of this ultimate approximation provide useful insights into fixpoints of the operator O. We then discuss applications of these results in logic programming.