On the declarative and procedual semantics of logic programs
Journal of Automated Reasoning
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
Logic programming as constructivism: a formalization and its application to databases
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
Three-valued formalizations of non-monotonic reasoning and logic programming
Proceedings of the first international conference on Principles of knowledge representation and reasoning
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
XSB as an efficient deductive database engine
SIGMOD '94 Proceedings of the 1994 ACM SIGMOD international conference on Management of data
Bottom-up evaluation and query optimization of well-founded models
Theoretical Computer Science
Tabled evaluation with delaying for general logic programs
Journal of the ACM (JACM)
An extension of Van Gelder's alternating fixpoint to magic programs
Journal of Computer and System Sciences
WFS + Branch and Bound = Stable Models
IEEE Transactions on Knowledge and Data Engineering
Characterizing D-WFS: Confluence and Iterated GCWA
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
Computing Well-founded Semantics Faster
LPNMR '95 Proceedings of the Third International Conference on Logic Programming and Nonmonotonic Reasoning
Characterizations of the Stable Semantics by Partial Evaluation
LPNMR '95 Proceedings of the Third International Conference on Logic Programming and Nonmonotonic Reasoning
The Deductive Database System LOLA
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Improving the Alternating Fixpoint: The Transformation Approach
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
LOLA - A Logic Language for Deductive Databases and its Implementation
Proceedings of the Second International Symposium on Database Systems for Advanced Applications
A Natural Semantics for Logic Programs with Negation
Proceedings of the Ninth Conference on Foundations of Software Technology and Theoretical Computer Science
A Classification Theory Of Semantics Of Normal Logic Programs: I. Strong Properties
Fundamenta Informaticae
A Classification Theory Of Semantics Of Normal Logic Programs: Ii. Weak Properties
Fundamenta Informaticae
On the equivalence and range of applicability of graph-based representations of logic programs
Information Processing Letters
Relating defeasible and normal logic programming through transformation properties
Theoretical Computer Science
A Rewriting Method for Well-Founded Semantics with Explicit Negation
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
Disjunctive Logic Programming: A Survey and Assessment
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part I
Equivalence in Answer Set Programming
LOPSTR '01 Selected papers from the 11th International Workshop on Logic Based Program Synthesis and Transformation
Nonmonotonic reasoning: towards efficient calculi and implementations
Handbook of automated reasoning
On the problem of computing the well-founded semantics
Theory and Practice of Logic Programming
Graphs and colorings for answer set programming
Theory and Practice of Logic Programming
Pruning Operators for Disjunctive Logic Programming Systems
Fundamenta Informaticae
Justifications for logic programs under answer set semantics
Theory and Practice of Logic Programming
Advanced Preprocessing for Answer Set Solving
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
A theory of forgetting in logic programming
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Computer Languages, Systems and Structures
Inspecting side-effects of abduction in logic programs
Logic programming, knowledge representation, and nonmonotonic reasoning
Rules and logic programming for the web
RW'11 Proceedings of the 7th international conference on Reasoning web: semantic technologies for the web of data
Justifications for logic programs under answer set semantics
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
Win-move is coordination-free (sometimes)
Proceedings of the 15th International Conference on Database Theory
Pruning Operators for Disjunctive Logic Programming Systems
Fundamenta Informaticae
Dealing with explicit preferences and uncertainty in answer set programming
Annals of Mathematics and Artificial Intelligence
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We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by BRASS and DIX (Brass and Dix, 1994; Brass and Dix, 1999) for disjunctive programs. However, even if we restrict their framework to nondisjunctive programs, their ‘residual program’ can grow to exponential size, whereas for function-free programs our ‘program remainder’ is always polynomial in the size of the extensional database (EDB). We show that particular orderings of our transformations (we call them strategies) correspond to well-known computational methods like the alternating fixpoint approach (Van Gelder, 1989; Van Gelder, 1993), the well-founded magic sets method (Kemp et al., 1995) and the magic alternating fixpoint procedure (Morishita, 1996). However, due to the confluence of our calculi (first noted in Brass and Dix, 1998), we come up with computations of the well-founded model that are provably better than these methods. In contrast to other approaches, our transformation method treats magic set transformed programs correctly, i.e. it always computes a relevant part of the well-founded model of the original program. These results show that our approach is a valuable tool to analyze, compare, and optimize existing evaluation methods or to create new strategies that are automatically proven to be correct if they can be described by a sequence of transformations in our framework. We have also developed a prototypical implementation. Experiments illustrate that the theoretical results carry over to the implemented prototype and may be used to optimize real life systems.