The well-founded 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 well-founded 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 well-founded 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 top-down 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...

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 SLDNF-resolution). If infinite failed trees are allowed then we obtain a method for the well-founded semantics. In both cases soundness and completeness are proved.

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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 well-founded 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 well-founded 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 counter-example. 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 ...

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 well-founded and Fitting semantics.

. We propose a new realization of goal-directed query evaluation of (non-floundering) normal logic programs for the well-founded semantics. To this end we introduce a new magic templates transformation and give a new fixed point characterization of the well-founded semantics, lifting an existing definition from the ground to the non-ground case. The new fixed point characterization enables us to show a step-by-step correspondence between the naive bottom-up evaluation of the transformed program and a class of top-down 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 bottom-up approach. 1 Introduction Bol and Degerstedt [BD93a] have proposed a concept of search forest to characterize a reasonably sized search space for goal-directed query evaluation ...

this paper we show that well-founded 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, 2-valued logic. Subsequently, we use this result to provide a constructive definition of well-founded 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 well-founded semantics, given entirely in terms of classical, 2-valued logic and thus, hopefully, dispel some of the

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 multi-predicate 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 semantics-preservative 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 `...