Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
On the relation between default and autoepistemic logic
Readings in nonmonotonic reasoning
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
Every logic program has a natural stratification and an iterated least fixed point model
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Bilattices and the semantics of logic programming
Journal of Logic Programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
On consistency and completeness of autoepistemic theories
Fundamenta Informaticae
Proceedings of the eleventh international conference on Logic programming
ACM Transactions on Database Systems (TODS)
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
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Reasoning with Incomplete Information
Reasoning with Incomplete Information
Epistemic Logic for AI and Computer Science
Epistemic Logic for AI and Computer Science
Uniform semantic treatment of default and autoepistemic logics
Artificial Intelligence
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
A Classification Theory Of Semantics Of Normal Logic Programs: Ii. Weak Properties
Fundamenta Informaticae
Erratum to 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
Artificial Intelligence
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic Programming
Fundamenta Informaticae
Predicate introduction under stable and well-founded semantics
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic Programming
Fundamenta Informaticae
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It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, that is, to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other nonmonotonic formalisms, such as auto-epistemic logic and default logic. In this work, we present a general, algebraic splitting theory for logics with a fixpoint semantics. Together with the framework of approximation theory, a general fixpoint theory for arbitrary operators, this gives us a uniform and powerful way of deriving splitting results for each logic with a fixpoint semantics. We demonstrate the usefulness of these results, by generalizing existing results for logic programming, auto-epistemic logic and default logic.