W. Chen, T. Swift, and D. S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--199, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....# i and # o and a (possibly partial) function f which maps sets of ground literals over # i into sets of ground literals over # o . There is a variety of query answering systems which can be used to compute answers to queries in A Prolog. A simple meta interpreter build on top of Prolog or XSB [10] proved to be sufficient for discuss them in this paper. The alternative approach which uses logic programs with well founded semantics and its extensions can be found in [1] At the end of the second stage the implementor will have a logic program # which, taken in conjunction with a collection ....

W. Chen, T. Swift and D. Warren, Efficient top-down computation of queries under the well-founded semantics, J. Logic Programming 24(3) (1995) 161--201.

.... sub derivations [2, 9, 35] The first problem with SLDNF resolution has been perfectly settled by the discovery of the well founded semantics [33] Two representative methods were then proposed for topdown evaluation of such a new semantics: Global SLS resolution [18, 22] and SLG resolution [6, 7]. Global SLS resolution is a direct extension of SLDNF resolution. It overcomes the semantic anomalies of SLDNF resolution by treating infinite derivations as failed and infinite recursions through negation as undefined. Like SLDNF resolution, it is linear for query evaluation. However, it ....

....set of clauses, called a system, into another system based on six basic transformation rules. A special class of literals, called delaying literals, is used to represent and handle temporarily undefined negative literals. Negative loops are identified by maintaining a dependency graph of subgoals [6, 7]. In contrast, SLT resolution is based on SLT trees in which the flow of the query evaluation is naturally depicted by the ordered expansions of tree nodes. It appears that this style of formulations is easier for users to understand and keep track of the computation. In addition, SLT resolution ....

W. D. Chen, T. Swift and D. S. Warren, Efficient top-down computation of queries under the well-founded semantics, Journal of Logic Programming 24(3):161-199 (1995).

....However, the framework is different, and algorithms are not addressed. Pollett and Remmel [29] consider logic programs with quantified Boolean formulas constraints, aiming at a more compact programming language rather than model representation. Query evaluation under der WFS using SLG resolution [4], implemented in the XSB system [30] is somewhat less related to our work, as it is a top down approach and, moreover, aims at answering a goal rather than representing the well founded model. It can be used to compute a residual program for query evaluation under stable model semantics [30] ....

W. Chen, T. Swift, and D. Warren. Efficient Top-Down Computation of Queries under the Well-Founded Semantics. Journal of Logic Programming, 24:161--199, 1995.

....the implementor will have a logic program which, taken in conjunction with a collection X of facts about known relations oe o . 2 There is a variety of query answering systems which can be used to compute answers to queries in A Prolog. A simple meta interpreter build on top of Prolog or XSB [10] proved to be sufficient for the purposes of this paper. Description of such a meta interpreter build on top of SLDNF of Prolog can be found in section 4. For more complicated programs, especially for those which have multiple stable models, this interpreter will go into a loop or answer unknown ....

W. Chen, T. Swift and D. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24,3:161--201, 1995.

....his goal without further interruptions. 3 REASONING ALGORITHMS The logic programming community has developed a large number of reasoning algorithms which range from the SLDNF resolution implemented 278 LOGIC BASED ARTIFICIAL INTELLIGENCE in traditional Prolog systems to the XSB resolution (Chen et al. 1995) implementing the well founded semantics (Van Gelder et al. 1991) and comparatively recent techniques which can be used for computing answer sets of A Prolog (Cholewi nski et al. 1996; Niemela and Simons, 1997; Faber et al. 1999; Wang and Zaniolo, 2000) The latter form the basis for answer ....

Chen, W., Swift, T., and Warren, D. (1995). Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--201.

....than the best systems) It is free and is available by anonymous ftp from URL:ftp: ftp.cs.sunysb.edu pub XSB . This is the first time that a negation different from negation asfinite failure (well founded semantics) has been incorporated into a complete PROLOG system. We refer the reader to [31, 33, 34, 77] for more detailed information. SLG resolution is very procedural in nature because it is based on tabling techniques. Roughly, given a query and a program it first computes a residual program with respect to the query. Under some assumptions (boundedterm size property and similar concepts) which ....

Weidong Chen, Terrance Swift, and David S. Warren. Efficient Top-Down Computation of Queries under the Well-Founded Semantics. Journal of Logic Programming, 24(3):219--245, 1995.

....The careful reader may have noticed that we did not at all incorporate the loop detection rule into our framework. The reason is that this rule is essentially the only non constructive rule that can only be approximated. For example Chen and Warren do such loop detection in their SLG or XSB system [CW95,CSW95,CW96] for non disjunctive programs (under WFS and STABLE) by tabling techniques. However, the main focus of this paper was to introduce the constraint machinery and to combine it with our former calculus. Loop detection is beyond the scope of this paper and we only give some hints in the next ....

Weidong Chen, Terrance Swift, and David S. Warren. Efficient Top-Down Computation of Queries under the Well-Founded Semantics. Journal of Logic Programming, 24(3):219--245, 1995.

....for a deterministic program (along a predetermined path of the SLD tree) views SLD as calls and returns from procedures (unifying atoms in a goal) To avoid looping, a tabling or memoing method is proposed. It has been reported in [4] for a deterministic program execution, and rediscovered in [5, 6, 7]. The concept is simple for a deterministic program: during the execution maintain a table of procedure calls (without side effects) and the values they return; if the same call is made during computation use the saved answer. For a nondeterministic program, one views the execution engine as ....

W.Chen, T.Swift, D.S.Warren, "Efficient Top-Down Computation of Queries under the Well-Founded Semantics", Dept. of Computer Science, SUNY at Stony Brook, Technical Report, 1993.

....The first Prolog interpreter was designed by Colmerauer in 1973; in 1977, David L. D. Warren developed a more efficient implementation of Prolog and made it available to others. The second query evaluation method mentioned here, SLG, was designed and implemented by Chen and David S. Warren [ Chen et al. 1995 ] The idea of negation as failure was introduced by Clark [1978] and the closed world assumption by Reiter [1978] Classical negation was incorporated into the syntax of logic programming rules by Gelfond and Lifschitz [1990] a similar idea was independently developed by Pearce and Wagner ....

Weidong Chen, Terrance Swift, and David Warren. Efficient topdown computation of queries under the well-founded semantics. Journal of Logic Programming, 24:161--199, 1995. 54

....1 Introduction Well founded semantics was introduced in [17] to provide 3 valued interpretations to logic programs with negation. Since its introduction, the well founded semantics has become one of the most widely studied and most commonly accepted approaches to negation in logic programming [1, 9, 5, 6, 18, 3]. It was implemented in several top down reasoning systems, most prominent of which is XSB [14] Well founded semantics is closely related to the stable model semantics [11] another major approach to logic programs with negation. The well founded semantics approximates the stable model semantics ....

W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--199, 1995.

....semantics has been proposed for non ground logic programs. The computation of stable models, based on the so called assume and reduce algorithm, is still relative to ground logic programs. But the computation of well founded semantics is for non ground logic programs. A prototype system called SLG [23] has been developed for goal oriented query evaluation under the well founded semantics. Given a query, SLG produces a residual program containing answers for all subgoals which are relevant to the query. In [24] SLG is extended to accommodate the stable model semantics. For a given query, SLG ....

W. Chen, T. Swift, and D. S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--199, 1995.

....the programming language PROLOG is based on logic programming. Disjunctive logic programming is one of the most expressive declarative logic programming language. Although PROLOG is not quite appropriate for disjunctive logic programs, other systems have been developed (such as the XSB system [CSW95] that allow disjunctive logic programs. We now present a translation from any domain description (D) in AK into a disjunctive logic program (D) and show that the translation (using answer set semantics [GL91] is sound and complete w.r.t. the semantics of AK . We have executed translations of ....

W. Chen, T. Swift, and D. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--201, 1995.

....in these formalisms must be developed. For years, despite tremendous advances in our understanding of nonmonotonic logics, implementation efforts and experimentation with nonmonotonic reasoning have been lagging behind. There are only few reported examples of such work [Poo88, Gin89, DdK89, CSW94, BNN 93] Recently, several algorithms to compute extensions were proposed [MT93, ALS94, Nie95, MNR95] In addition, several systems for default reasoning were implemented and are publicly available (DeReS [CMMT95a] smodels [NS95] FROST [EFK 95] However, one of the main problems in ....

W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 1994.

....by those algorithms. The algorithms show striking analogies to the Davis Putnam procedure for testing satisfiability of CNF formulas. One of these algorithms is similar to the algorithm recently described and studied in [7, 8] There are also some analogies with the algorithms described in [9, 3]. Additional motivation comes from considerations of expressive power of logic programming and of representability issues. Both concepts help understand the scope of applicability of logic programming as a knowledge representation tool. Disjunctive logic programs with answer set semantics (logic ....

....the unions of M and stable models of P 0 . There are several specific choices for the procedure implied set. A trivial option is to return M = and P 0 = P . Another possibility is to output as M the set of atoms true in the well founded semantics and as P 0 the residual program for P (see [9, 3]) However, in general, there are many other, intermediate, ways to compute M and P 0 in polynomial time so that conditions (1) and (2) above are satisfied. We will now describe the algorithms. We adopt the following notation. For a logic program clause r, by head(r) we denote the head of r and ....

W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24:161--200, 1994.

....and methods of programming in these formalisms must be developed. For years, despite tremendous advances in our understanding of nonmonotonic logics, implementation efforts and experimentation with nonmonotonic reasoning have been lagging behind. There are only few reported examples of such work [17, 11, 9, 8, 3]. Recently, several algorithms to compute extensions were proposed [14, 1, 15, 13] In addition, several systems for default reasoning were implemented and are publicly available (DeReS [6] smodels [16] FROST [10] However, one of the main problems in the efforts to develop reasoning systems ....

W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 1994.

....users, the ftp directory and web site contain papers covering in detail various aspects of tabling. An overview of SLG resolution, and a practical evaluation strategy for it are provided in [7, 28] 30, 29, 24, 15, 34, 26] describe fully the SLG WAM as it is implemented in Version 1.7. 1, and [35, 6] analyze its performance. 5.1 SLG Evaluation 5.1.1 Tabling Consider the Prolog program ancestor(X,Y) parent(X,Y) ancestor(X,Y) ancestor(X,Z) parent(Z,Y) together with the query ancestor(1,Y) This program has a simple, declarative meaning: Y is an ancestor of X if Y is a parent of ....

W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. J. Logic Programming, 24(3):161--199, September 1995.

.... well founded semantics [1, 10, 7, 28] In particular, SLG resolution [7] not only has various desirable theoretical properties, including goal orientedness, polynomial time data complexity, answer sharing and preservation of all three valued stable models, but also has been implemented efficiently [6, 25, 27], delivering excellent performance for query evaluation. This section discusses informally how to extend SLG resolution [7] with constructive negation. For simplicity, we consider query evaluation for only function free programs. 4.1. Tabled Evaluation with Constraints Given a function free ....

W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--199, September 1995.

....a key implementation issue is how to handle negative literals. An incremental technique has been developed for efficient detection of subgoals that are completely evaluated (so that their negative counterparts can be solved) and subgoals that are possibly involved in loops through negation [3]. A formal treatment of SLG resolution (for normal logic programs possibly containing function symbols) is presented in [5] It is shown that SLG resolution preserves all three valued stable models, including the well founded partial model as a special case. The contribution of this paper is two ....

....cost of query evaluation. In practice, the portion of a program that is relevant to a query is much smaller than the original program. Efficient techniques for incremental detection of subgoals that are completely evaluated or are possibly involved in negation through recursion have been developed [3]. 5.3 Implementation A preliminary implementation of SLG 8 resolution has been carried out by extending a Prolog meta interpreter for SLG resolution of normal logic programs [6] The SLG meta interpreter employs an efficient algorithm for incremental maintenance of dependencies among subgoals so ....

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Chen, W., Swift, T., and Warren, D.S. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 1995. to appear.

....[82] 53] 64] 134] 16] 13] 17] 18] 119] 110] 120] 136] Clear progress from Definite LPs, through Stratified and Normal LPs to Abductive LPs, Disjunctive LPs, and Quantitative LPs. Implementation and Systems [8] 129] 79] 49] 67] 98] 121] 109] 39] 9] [22], 51] 133] 99] 135] 101] 52] 42] 43] 54] 93] 107] 108] 31] XSB, YAP, Lola, and others Optimizations [36] 5 Overview ffl Magic Sets and Related Research (e.g. Alexander Method) Formulation [102] 7] 111] 124] 20] 87] 85] 10] 70] 91] 117] ....

W. Chen, T. Swift, and D. S. Warren. Efficient top-down computation of queries under the well-founded semantics. J. Logic Programming, 24(3):161--199, September 1995.

....of research into it. Tabling and Related Research Formulation [41] 17] 108] 38] 60] 98] 115] 120] 15] 14] 20] 22] 33] 19] 105] 34] 94] 54] 110] 23] 27] Implementation and Systems [6] 116] 64] 42] 2] 55] 82] 84] 106] 107] 93] 7] [21], 43] 44] 96] 121] 45] 83] 95] 92] Optimizations [30] 6 Motivation Magic Sets and Related Research (e.g. Alexander Method) Formulation [87] 5] 97] 111] 18] 69] 67] 8] 59] 73] 103] 39] 49] 79] 9] 101] 89] 66] Implementation and Systems [6] ....

....3 2.2 2.1 2.1 2.2 a V1 V1 V2 rt(b,V,d) rt(a,g(b,c) c) rt(a,f(a,b) a) rt(a,f(a,V) V) Tries allow check insert in a single pass and makes the duplicate check nearly costless. 80 Implementation of Tabling Issue: How to incrementally complete a table. ffl XSB uses a stack based mechanism [21] ffl Vanilla Magic uses a statically defined control strategy. ffl Ordered search uses a dynamic control strategy [79] Issue: How to handle unknown undefined literals ffl One issue involves dynamically changing the computation rule ffl A second issue involves representing atoms that are ....

W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. J. Logic Programming, 24(3):161--199, September 1995.

....avoided. The use of negative contexts, however, prevents the full sharing of answers of a subgoal across different negative 1 contexts. In the worst case, a subgoal may be evaluated in a number of negative contexts that is exponential in the size of the Herbrand base of a function free programs [11]. Techniques for effective set at a time query evaluation have been studied in deductive databases, including magic sets [4, 5] magic templates [33] and Alexander templates [39] The main idea is to simulate top down SLD resolution to avoid generation of tuples irrelevant to the given goal. In ....

....PE is a ground fact, with an empty body. In addition, N (1) is polynomial in the size of PE . 2 40 In practice, efficient incremental algorithms have been developed that detect subgoals that are completely evaluated or are possibly involved in loops through negation in a constant amount of time [11]. We believe that the freedom of choosing an arbitrary computation rule and choosing an arbitrary strategy of selecting transformations in SLG resolution offers the maximum flexibility for practical implementations. 6 Restricted SLG Resolution SLG resolution provides a general framework for ....

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W. Chen, T. Swift, and D.S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 1994. to appear.

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W. Chen, T. Swift, and D. S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--199, 1995.

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W. Chen, D. Warren. Efficient top-down computation of queries under the well-founded semantics. J. ACM, 43(1): 20-74, 1996.

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W. Chen, T. Swift, and D. S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3):161--199, 1995.

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Weidong Chen, Terrance Swift, and David S. Warren. Efficient Top-Down Computation of Queries under the Well-Founded Semantics. Journal of Logic Programming, 24(3):219--245, 1995.

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