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Efficient TopDown Computation of Queries under the WellFounded Semantics
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... The wellfounded model provides a natural and robust semantics for logic programs with negative literals in rule bodies. Although various procedural semantics have been proposed for query evaluation under the wellfounded semantics, the practical issues of implementation for effective and efficient ..."
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Cited by 81 (12 self)
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The wellfounded model provides a natural and robust semantics for logic programs with negative literals in rule bodies. Although various procedural semantics have been proposed for query evaluation under the wellfounded semantics, the practical issues of implementation for effective and efficient computation of queries have been rarely discussed. This paper investigates two major implementation issues of query evaluation under the wellfounded semantics, namely (a) to ensure that negative literals be resolved only after their positive counterparts have been completely evaluated, and (b) to detect and handle potential negative loops. We present efficient incremental algorithms for maintaining positive and negative dependencies among subgoals in a topdown evaluation. Both completely evaluated subgoals and potential negative loops are detected by inspecting the dependency information of a single subgoal. Our implementation can be viewed as an effective successor to SLDNF resolution, ex...
What is Failure? An Approach to Constructive Negation
, 1994
"... A standard approach to negation in logic programming is negation as failure. Its major drawback is that it cannot produce answer substitutions to negated queries. Approaches to overcoming this limitation are termed constructive negation. This work proposes an approach based on construction of failed ..."
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Cited by 54 (4 self)
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A standard approach to negation in logic programming is negation as failure. Its major drawback is that it cannot produce answer substitutions to negated queries. Approaches to overcoming this limitation are termed constructive negation. This work proposes an approach based on construction of failed trees for some instances of a negated query. For this purpose a generalization of the standard notion of a failed tree is needed. We show that a straightforward generalization leads to unsoundness and present a correct one. The method is applicable to arbitrary normal programs. If finitely failed trees are concerned then its semantics is given by Clark completion in 3valued logic (and our approach is a proper extension of SLDNFresolution). If infinite failed trees are allowed then we obtain a method for the wellfounded semantics. In both cases soundness and completeness are proved.
WellFounded and Stationary Models of Logic Programs
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 1994
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A Compositional Proof Method of Partial Correctness for Normal Logic Programs with an application to Gödel
 B , 12th Int. Logic Programming Symp
, 1995
"... This report presents a new proof method of partial correctness for logic programs with negation based on a proof modularity. We prove in a compositional way that Fitting's or the wellfounded semantics of the program is included in a specification. We give conditions for an abstract semantics t ..."
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Cited by 10 (1 self)
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This report presents a new proof method of partial correctness for logic programs with negation based on a proof modularity. We prove in a compositional way that Fitting's or the wellfounded semantics of the program is included in a specification. We give conditions for an abstract semantics to be compositional and we base our proof method on this property. We present also conservative but compositional extensions of Fitting's and of the wellfounded semantics. As an illustration, an application is made to the module system of the Godel language. Moreover, our method is suitable for incremental validation since it does not require all parts of the program to be implemented. This document is an extended version of [9] which incorporates the missing proofs and a counterexample. R'esum'e Ce rapport pr'esente une nouvelle m'ethode de preuve de correction partielle pour des programmes logiques avec n'egation bas'ee sur des preuves modulaires. Nous montrons de fa¸con compositionelle que ...
Unfolding the Wellfounded Semantics
 Journal of Electrical Engineering, Slovak Academy of Sciences
, 2002
"... We study the xpoint completion, proposed by Dung and Kanchanasut in [DK89]. The fixpoint completion is a program transformation  it performs a kind of unfolding of recursion through positive atoms in the clauses of a program f that was shown to preserve the semantics of a program in a certain sense ..."
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Cited by 8 (1 self)
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We study the xpoint completion, proposed by Dung and Kanchanasut in [DK89]. The fixpoint completion is a program transformation  it performs a kind of unfolding of recursion through positive atoms in the clauses of a program f that was shown to preserve the semantics of a program in a certain sense. We generalize the results from [DK89] in some ways and show how the handling of negation is transformed by the fixpoint completion. We thereby obtain a more clarified view of both the fixpoint completion itself and the relationship between wellfounded and Fitting semantics.
Magic Computation for Wellfounded Semantics
 Nonmonotonic Extensions of Logic Programming, LNAI 927
, 1995
"... . We propose a new realization of goaldirected query evaluation of (nonfloundering) normal logic programs for the wellfounded semantics. To this end we introduce a new magic templates transformation and give a new fixed point characterization of the wellfounded semantics, lifting an existing def ..."
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Cited by 4 (0 self)
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. We propose a new realization of goaldirected query evaluation of (nonfloundering) normal logic programs for the wellfounded semantics. To this end we introduce a new magic templates transformation and give a new fixed point characterization of the wellfounded semantics, lifting an existing definition from the ground to the nonground case. The new fixed point characterization enables us to show a stepbystep correspondence between the naive bottomup evaluation of the transformed program and a class of topdown search strategies defined in terms of the search forest framework of Bol and Degerstedt. This correspondence implies that the magic transformation is sound and complete. Hence, it provides an upper bound on the search space that must be considered in order to preserve completeness of the bottomup approach. 1 Introduction Bol and Degerstedt [BD93a] have proposed a concept of search forest to characterize a reasonably sized search space for goaldirected query evaluation ...
Two Simple Characterizations of WellFounded Semantics
 Proceedings of the International Conference on Mathematical Foundations of Computer Science (MFCS'92
, 1995
"... this paper we show that wellfounded models can also be defined as fixed points of a natural program transformation (factorization) which is completely analogous to the transformation used in the definition of stable models and is expressed entirely in terms of classical, 2valued logic. Subsequentl ..."
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Cited by 1 (0 self)
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this paper we show that wellfounded models can also be defined as fixed points of a natural program transformation (factorization) which is completely analogous to the transformation used in the definition of stable models and is expressed entirely in terms of classical, 2valued logic. Subsequently, we use this result to provide a constructive definition of wellfounded models as fixed points of an iterative factorization procedure. We note that no such constructive characterization is available for stable models which are computationally intractable even in the class of propositional programs [KS89, MT88]. The results obtained in this paper, coupled with our earlier result showing that the wellfounded semantics can be equivalently defined by means of first order completions of logic programs [Prz91c], provide natural and simple characterizations of wellfounded semantics, given entirely in terms of classical, 2valued logic and thus, hopefully, dispel some of the
An efficient validation mechanism for Inductive Logic Programming using compositionality
, 1995
"... Inductive Logic Programming, which consists in learning clauses from examples, can be viewed as a cycle conception/validation leading to the acceptance of the induced program provided that it fulfills a certain criterion. We focus on the validation step in the context of empirical multipredicate le ..."
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Inductive Logic Programming, which consists in learning clauses from examples, can be viewed as a cycle conception/validation leading to the acceptance of the induced program provided that it fulfills a certain criterion. We focus on the validation step in the context of empirical multipredicate learning of normal clauses. Thanks to a compositional semantics, the classical validation step of the complete induced program can be replaced by the verification of local properties for a cut out into units, considerably limiting the usual combinatorial explosion. Moreover, we provide a semanticspreservative transformation which allows to simplify the program and provides a further refinement of the cut out. R'esum'e La Programmation Logique Inductive consiste `a apprendre des clauses `a partir d'exemples et peut etre vue comme un cycle conception/validation menant `a l'acceptation du programme induit d`es qu'il satisfait un certain crit`ere. Nous nous int'eressons plus particuli`erement `...