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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...
Tabulated Resolution for Well Founded Semantics
 Journal of Logic Programming
, 1993
"... Based on the search forest for positive programs as defined by Bol and Degerstedt, we define a tabulated version of SLSresolution that is sound and complete w.r.t. well founded semantics. In contrast to SLSresolution as proposed by Przymusinski and by Ross, a positivistic computation rule is not ..."
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Cited by 51 (2 self)
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Based on the search forest for positive programs as defined by Bol and Degerstedt, we define a tabulated version of SLSresolution that is sound and complete w.r.t. well founded semantics. In contrast to SLSresolution as proposed by Przymusinski and by Ross, a positivistic computation rule is not required. This proposal is closely related to that of Chen and Warren, but it relies on tabulation for both positive and negative recursion. In this way, only one forest needs to be constructed, rather than a forest for each negative context. For functionfree programs, the resulting search forest is finite. Keywords: logic programming, deductive databases, well founded semantics, tabulation, search forest, SLSresolution, implementation. 1 Introduction It was shown in [5, 24] that bottomup computation with magic templates [2, 22] and tabulated SLDresolution [9, 26, 27] perform `essentially' the same computation. This result is made more precise in [4], where a common framework for both ...
Computation of Stable Models and its Integration with Logical Query Processing
 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
, 1994
"... The wellfounded semantics and the stable model semantics capture intuitions of the skeptical and credulous semantics in nonmonotonic reasoning, respectively. They represent the two dominant proposals for the declarative semantics of deductive databases and logic programs. However, neither semant ..."
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Cited by 48 (5 self)
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The wellfounded semantics and the stable model semantics capture intuitions of the skeptical and credulous semantics in nonmonotonic reasoning, respectively. They represent the two dominant proposals for the declarative semantics of deductive databases and logic programs. However, neither semantics seems to be suitable for all applications. We have developed an efficient implementation of goaloriented effective query evaluation under the wellfounded semantics. It produces a residual program for subgoals that are relevant to a query, which contains facts for true instances and clauses with body literals for undefined instances. This paper presents a simple method of stable model computation that can be applied to the residual program of a query to derive answers with respect to stable models. The method incorporates both forward and backward chaining to propagate the assumed truth values of ground atoms, and derives multiple stable models through backtracking. Users are ab...
An abstract machine for computing the wellfounded semantics
 Proceedings of the Joint International Conference and Symposium on Logic Programming
, 1996
"... The wellfounded semantics has gained wide acceptance partly because it is a skeptical semantics. That is, the wellfounded model posits as unknown atoms which are deemed true or false in other formalisms such as stable models. This skepticism makes the wellfounded model not only useful in itself, ..."
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Cited by 31 (17 self)
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The wellfounded semantics has gained wide acceptance partly because it is a skeptical semantics. That is, the wellfounded model posits as unknown atoms which are deemed true or false in other formalisms such as stable models. This skepticism makes the wellfounded model not only useful in itself, but also suitable as a basis for other forms of nonmonotonic reasoning. For instance, since algorithms to compute stable models are intractable, the atoms relevant tosuch algorithms can be limited to those unde ned in the wellfounded model. This paper presents an implementation ofthewellfounded semantics in the SLGWAM of XSB. To compute the wellfounded semantics, the SLGWAM adds three operations to its tabling engine  negative loop detection, delay and simplication  which serve to detect, to break and to resolve cycles through negation that may arise in evaluating normal programs. We describe fully the addition of these operations to our tabling engine, and demonstrate the e ciency of our implementation in two ways. First, we present a theorem that bounds the need for delay to those literals which are not dynamically strati ed for a xedorder computation. Secondly, we present performance results that indicate that the overhead of delay and simpli cation to Prolog  or tabled  evaluations is minimal. 1
WellFounded and Stationary Models of Logic Programs
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 1994
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Formalizing a logic for logic programming
 Annals of Mathematics and Artificial Intelligence
, 1992
"... ..."
Deterministic and NonDeterministic Stable Models
 Journal of Logic and Computation
, 1997
"... Stable models have been first introduced in the domain of total interpretations (T stable models), where the existence of multiple Tstable models for the same program provides a powerful mechanism to express nondeterminism. Stable models have been later extended to the domain of partial interpre ..."
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Cited by 26 (6 self)
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Stable models have been first introduced in the domain of total interpretations (T stable models), where the existence of multiple Tstable models for the same program provides a powerful mechanism to express nondeterminism. Stable models have been later extended to the domain of partial interpretations (Pstable models). In this paper, we show that the presence of multiple Pstable models need not be a direct manifestation of nondeterminism, for it can be instead an expression of assorted degrees of undefinedness. To separate the two factors, nondeterminism and undefinedness, this paper introduces the notion of deterministic stable models and strictly nondeterministic ones. Deterministic stable models form an interesting family, having a lattice structure where the wellfounded model serves as the bottom; the top of the lattice, the maximum deterministic stable model, resolves differences between any two Pstable models in the family. On the other hand, every two models in a fam...
Bottomup Evaluation and Query Optimization of WellFounded Models
 Theoretical Computer Science
, 1995
"... We present a bottomup operational procedure for computing wellfounded models of allowed programs with negation. This procedure provides a practical method of handling programs that involve unstratified negation in a manner that may be mixed with other evaluation approaches, such as seminaive eval ..."
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Cited by 26 (1 self)
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We present a bottomup operational procedure for computing wellfounded models of allowed programs with negation. This procedure provides a practical method of handling programs that involve unstratified negation in a manner that may be mixed with other evaluation approaches, such as seminaive evaluation and various program transformations. We define classes of programs and sideways information passing strategies (sips) for which the magic sets transformation preserves wellfounded models with respect to the query. The classes of programs and sips we consider strictly subsume those already considered in the literature, and include stratified programs (with any choice of sips), lefttoright modularly stratified programs (with leftto right sips) and arbitrary programs (with wellfounded sips). For these programs and sips, our procedure for computing wellfounded models is applicable to the rewritten programs, thus allowing increased efficiency by specializing a program for a query. Fi...
The Underlying Search for Magic Templates and Tabulation
 Proceedings of the Tenth International Conference on Logic Programming
, 1993
"... The main aim of this paper is to present a framework for tabulated SLDresolution that allows a strict separation between search space and search. We introduce the notion of a search forest to model the search space, and we define what we understand by a search strategy for it. We present some basic ..."
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Cited by 25 (3 self)
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The main aim of this paper is to present a framework for tabulated SLDresolution that allows a strict separation between search space and search. We introduce the notion of a search forest to model the search space, and we define what we understand by a search strategy for it. We present some basic search strategies and discuss how a particular tabulation technique, OLDTresolution, and a particular transformation technique, Magic Templates, relate to our approach. This comparison also reveals an inherent difference between the tabulation and the transformation approach. 1 Introduction Resolution is the main technique used by query answering systems for logic programs. It can be applied in two different ways, usually called "bottomup " and "topdown". The topdown methods are perhaps the most intuitive ones, because their starting point is the query: they are goaloriented . As a result they will not compute irrelevant facts, but intermediate results that are needed several times ca...
The Limits of FixedOrder Computation
 Theoretical Computer Science
, 1996
"... . Fixedorder computation rules, used by Prolog and most deductive database systems, do not suffice to compute the wellfounded semantics [19] because they cannot properly resolve loops through negation. This inadequacy is reflected both in formulations of SLSresolution [8, 12] which is an ideal se ..."
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Cited by 23 (18 self)
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. Fixedorder computation rules, used by Prolog and most deductive database systems, do not suffice to compute the wellfounded semantics [19] because they cannot properly resolve loops through negation. This inadequacy is reflected both in formulations of SLSresolution [8, 12] which is an ideal search strategy, and in more practical strategies like SLG [3], or WellFounded Ordered Search [16]. Typically, these practical strategies combine an inexpensive fixedorder search with a relatively expensive dynamic search, such as an alternating fixpoint [18]. Restricting the search space of evaluation strategies by maximizing the use of fixedorder computation is of prime importance for efficient goaldirected evaluation of the wellfounded semantics. Towards this end, the theory of modular stratification [13], formulates a subset of normal logic programs whose literals can be statically reordered so that the program can be evaluated using a fixedorder computation rule. However, exploratio...