Kemp D. B., Stuckey P. J., and Srivastava D. Magic sets and bottom-up evaluation of wellfounded models. In Proceedings of the 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....(in terms of intermediates facts (subgoals) that are generated [Sek89, RSS90, Cod97] which retains the advantages of avoiding in nite loops and set at a time computations. They also study semantic models and magic transformations for deductive database languages with negation [KSS95, KSS92, KSS91] Thus, we may say that the bottom up evaluation is better than top down one w.r.t. positive goals: bottom up evaluation is a complete deduction procedure when top down is not. In the presence of function symbols and negative goals, both bottom up and top down evaluation with negative goals are, ....

D. Kemp, D. Srivastava, and P. Stuckey. Magic Sets and Bottom-up Evaluation of Well-founded Models. In Proc. of ILPS, pages 337-354. MIT Press, 1991.

....have been investigated for stratified and modularly stratified programs [3, 34, 37] With negation, the major issue becomes maintaining dependencies among magic tuples (or subgoals) so as to ensure that a positive subgoal be fully evaluated before its negative counterpart is solved. Kemp et al. [18] developed a technique that computes the wellfounded partial model using a doubled program, one for deriving definitely true answers and the other for deriving potentially true answers. The doubled program technique may make too many magic facts true, which means that more subgoals are evaluated ....

....) and q(f(g(a) may be treated as calls of the same binding pattern when they are obtained from q(f(X) by binding X to g(Y ) and g(a) respectively, even though one subsumes the other. For general programs, the magic sets transformation does not always preserve the wellfounded semantics [18]. The proposed solutions in [18, 19] use a doubled program, one for computing definitely true facts and the other for computing not definitely false facts. The separate computation of these two classes of facts may cause redundant inferences since the sets of not definitely false facts are ....

[Article contains additional citation context not shown here]

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic sets and bottom-up evaluation of well-founded models. In Intl. Logic Programming Symposium, pages 337--351, 1991.

....Work A problem similar to the one discussed in this paper, is doing magic sets transformation on datalog programs with stratified negation and ensuring that the negation remains stratified. Similarly, ensuring the same well founded semantics of a program before and after MST, has been treated in [Ros90, KSS91]. In [BPRM91] the authors describe a labeling algorithm and transformation on the programs to ensure that the MST of a stratified program is also stratified. The labeling algorithm identifies all negated predicates that also occur positively and fully replicates the negated instances, ....

....4. However, our method for doing restricted replication could also reduce the number of negated predicates replicated by [BPRM91] Another alternative for ensuring that the MST of a nonrecursive program is nonrecursive, is to use a SIPS that ensures the condition. The idea of a well founded SIPS [KSS91] is useful here. Informally, if the SIPS used in the program respects the stratification, then information passing will be in the same direction as the dependencies and therefore MST will not introduce cycles. However, often this SIPS is not the most desirable one, and in general we need a way of ....

D.B. Kemp, P.J. Stuckey, and Divesh Srivastava. Magic-Sets and Bottom-Up Evaluation of Well-Founded Models. In International Symposium on Logic Programming, 1991.

....program corresponds, step by step, to a class of search strategies, called magic strategies, for non floundering queries. As a consequence, the well founded model of the transformed program is shown to be sound and complete wrt a given program and query. Unlike Kemp, Stuckey and Srivastava [KSS91], KSS92] and Morishita [Mor93] our goal is not to describe a specific algorithm for computing answers to queries. Our aim is rather (1) to define an upper bound on the search space needed to compute answers bottom up using magic templates and (2) to relate the magic approach to the search ....

D. Kemp, P. Stuckey, and D. Srivastava. Magic Sets and Bottom-up Evaluation of Well-founded Models. In Proc. of 1991 International Logic Programming Symposium, San Diego, pages 337--351. The MIT Press, 1991.

....mechanisms, however, prohibit the full sharing of answers to subgoals across different negative contexts in the nested fixpoint computation. Although simple to implement, they may cause exponential behavior in the worst case [6] Bottom up computation of the well founded semantics has been studied [10, 11, 13, 15]. These approaches are based upon either van Gelder s alternating fixpoint characterization of the well founded model [25] or the fixpoint for the least three valued stable model [4, 17] Due to the single fixpoint computation, all answers of subgoals can be shared. Each iteration of the fixpoint ....

....which is similar to SLG resolution [5] One interesting aspect of the approach in [3] is that non ground negative literals are also returned as part of answers. This allows a more flexible handling of some queries that would be floundered in SLG resolution. The bottom up techniques presented in [10, 11, 13, 15] evaluate queries according to the alternating fixpoint [25] or the least three valued stable model [4, 17] in a more direct manner. The magic sets technique in [10, 11] may make too many magic facts true, and thus evaluate subgoals that are irrelevant. The improvement proposed in [13] ....

[Article contains additional citation context not shown here]

Kemp, David B., Stuckey, Peter J., and Srivastava, Divesh. Magic sets and bottom-up evaluation of well-founded models. In Intl. Logic Programming Symposium, pages 337--351, 1991.

....systems and interesting test cases for such systems is collected as a project of the artificial intelligence group at Koblenz. We refer to http: www.uni koblenz.de ag ki LP . 6. 1 Non Disjunctive Semantics There are many theoretical papers that deal with the problem of implementation ([BD93,KSS91,DN95,FLMS93]) but only a few running systems. The problem of handling and representing ground programs given a non ground one has also been addressed [KNS94,KNS95,EGLS96] In [BNNS93,BNNS94] the authors showed how the problem of computing stable models can be transformed to an Integer Linear Programming ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT, June 1991.

....however, prohibit the full sharing of answers to subgoals across different negative contexts in the nested fixpoint computation. Although simple to implement, they may cause exponential behavior in the worst case [7] Bottom up computation of the well founded semantics has also been studied [10, 11, 13, 15]. These approaches are based upon either van Gelder s alternating fixpoint characterization of the well founded model [28] or the fixpoint for the smallest three valued stable model [4, 17] Due to the single fixpoint computation, all answers of subgoals can be shared. Each iteration of the ....

....which is similar to SLG resolution [6] One interesting aspect of the approach in [3] is that non ground negative literals are also returned as part of answers. This allows a more flexible handling of some queries that would be floundered in SLG resolution. The bottom up techniques presented in [10, 11, 13, 15] evaluate queries according to the alternating fixpoint [28] or the smallest three valued stable model [4, 17] in a more direct manner. The magic sets technique in [10, 11] may make too many magic facts true, and thus evaluate subgoals that are irrelevant. The improvement proposed by Morishita ....

[Article contains additional citation context not shown here]

Kemp, David B., Stuckey, Peter J., and Srivastava, Divesh. Magic sets and bottomup evaluation of well-founded models. In Intl. Logic Programming Symposium, pages 337--351, 1991.

....Work A problem similar to the one discussed in this paper, is doing magic sets transformation on datalog programs with stratified negation and ensuring that the negation remains stratified. Similarly, ensuring the same well founded semantics of a program before and after MST, has been treated in [KSS91], Ros90] In [BPRM91] the authors describe a labelling algorithm and transformation on the programs to ensure that the MST of a stratified program is also stratified. The labelling algorithm identifies all negated predicates that also occur positively and fully replicates the negated instances, ....

....3. However, our method for doing restricted replication could also reduce the number of negated predicates replicated by [BPRM91] Another alternative for ensuring that the MST of a nonrecursive program is nonrecursive, is to use a SIPS that ensures the condition. The idea of a well founded SIPS [KSS91] is useful here. Informally, if the SIPS used in the program respects the stratification, then information passing will be in the same direction as the dependencies and therefore MST will not introduce cycles. However, often this SIPS is not the most desirable one, and in general we need a way of ....

D.B. Kemp, P.J. Stuckey, and Divesh Srivastava. Magic-Sets and Bottom-Up Evaluation of Well-Founded Models. In International Symposium on Logic Programming, 1991.

....1) succ(3; 2) Since rule r2 can be instantiated with the same value for X and Y , this program is not locally stratified. However, it is modularly stratified. The evaluation of the magic sets transformation of this class of programs has also been considered in the literature ( Bry89, Ros90, KSS91, RSS92a] 2 The well founded model [VRS91] is a general approach to assigning semantics to a logic program that generalizes the approaches based on stratification. The well founded model of a program can be 3 valued, assigning the truth value unknown to some atoms. However, it coincides with ....

David Kemp, Divesh Srivastava, and Peter Stuckey. Magic sets and bottom-up evaluation of wellfounded models. In Proceedings of the International Logic Programming Symposium, pages 337--351, San Diego, CA, U.S.A., October 1991.

....understood on the source code level. Of course, specialized data structures can be useful for improving the efficiency, but they are not necessary for understanding the correctness of the method. Our algorithm has a strong relation to the classical alternating fixpoint procedure, which was used in [KSS91] for bottom up computation of the (non disjunctive) WFS. More precisely, they restrict the conditional facts to the head literal and a one bit indication whether there is a non trivial body or not. This is done by managing two versions of every predicate: the certainly true facts and the possibly ....

....there is a non trivial body or not. This is done by managing two versions of every predicate: the certainly true facts and the possibly true facts. Of course, this is a loss of information, but it can be compensated by recomputing the conditional facts for every step of the reduction phase. In [KSS91], also the optimization is used that they start with the computation of certainly true facts, and then the first computation of the possibly true facts can be combined already with the first reduction. Even for non disjunctive programs, there can be exponentially many derivable conditional facts ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT, June 1991.

....transformational approaches have been considered in [DM93, CL95, DN95] While in [DM93] abstract properties have been used only for speeding up query evaluation, in [CL95] the main focus of the program transformation is to make explicit possible uses of disjunctive information. The authors of [DN95, KSS91] consider only non disjunctive programs under the well founded semantics. The first step of our approach is to compute the set of implied conditional facts [Bry89, Bry90, DK89a, DK89b, HY91] These are rules without positive body literals, which result from delaying the evaluation of negative ....

....Of course, it is not necessary to have a strict separation between the first and the second step of the approach. By mixing and optimizing them, we are also able to derive the standard bottom up query evalution algorithm for stratified non disjunctive programs and the algorithm proposed in [KSS91] for the WFS of non disjunctive programs. We believe that our approach can be a good framework to understand and compare other proposed (bottom up) query evaluation algorithms. Only the few atoms which are undefined in the WFS are considered in the third step. We propose to compute an appropriate ....

[Article contains additional citation context not shown here]

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic sets and bottom-up evaluation of well-founded models. In Proc. of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT Press, 1991.

....systems and interesting test cases for such systems is collected as a project of the artificial intelligence group at Koblenz. We refer to http: www.uni koblenz.de ag ki LP . Non Disjunctive NMR Semantics There are many theoretical papers that deal with the problem of implementation ([BD93, KSS91, DN95, FLMS93]) but only few running systems. The problem of handling and representing ground programs given a non ground one 7 WHAT DO WE WANT AND WHAT IS IMPLEMENTED 75 has also been adressed [KNS94, KNS95, ELS97] In [BNNS93, BNNS94] the authors showed how the problem of computing stable models can be ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT, June 1991.

....of the program Phi, i.e. it is equivalent under the D WFS and any other semantics with these properties. Theorem 4.3 is our main result. We also define a weaker variant of Phi called Phi and use it to define WD WFS, a semantics which extends WFS and WGCWA. For non disjunctive programs, [KSS91] proposed a bottom up algorithm for computing the well founded semantics. The main difference is that they do not explicitly use conditional facts, but recompute them implicitly while performing the reductions. Finally, bottom up query evaluation for disjunctive default theories was investigated ....

....in preparation. First, it seems that every query evaluation algorithm which is able to handle non stratified programs has to delay negative ground literals under certain conditions. For instance, this is done in [CW93a] Second, our algorithm has a strong relation to the algorithm proposed in [KSS91] for bottom up computation of the (non disjunctive) WFS. More precisely, they restrict the conditional facts to the head literal and one bit indication wether there is a non trivial body or not. They do this by managing two versions of every predicate: The certainly true facts and the possibly ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic sets and bottom-up evaluation of well-founded models. In Proc. of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT Press, 1991.

....TU Tree for p; and successful otherwise. 4 In the sequel we assume, without loss of generality, that the only fact of a program is true. Other facts of programs are translated into rules with true in the body. 5 A similar idea, but in the context of bottom up procedures, is expounded in [14]. The only TU Tree for p is p0 u not p; and so there is a recursion in p through negation by default. So p in the TU Tree is assigned the status successful, and consequently not p in the T Tree is failed. Thus the proof of verity for p fails. The formalization of these solutions, presented ....

....based on modular partial evaluation rewrite rules for top down query evaluation under WFS; it focuses on positive goals, and delays non ground negative ones. Our approach, in contrast, is akin to a semantic tree refutation method. The notion of doubled program was first introduced in [14] but in the context of bottom up evaluation. They showed that magic sets transformations do not preserve well founded semantics and described a technique in [15] applicable to the class of normal programs. Eshgi and Kowalski s abductive procedure [11] corrected in [10] is sound wrt to preferred ....

D. B. Kemp, P. J. Stuckey, and D. Srivastava. Magic sets and bottom-up evaluation of well--founded models. In Proc. ILPS'91, pages 337--351. MIT Press, 1991.

....and a pure depth first search. Their technique, called Ordered Search, also maintains subgoal dependency information, and handles programs with left to right modularly stratified negation. For general programs, the magic sets transformation does not always preserve the well founded semantics [14]. Methods proposed in [14, 15] to solve this problem, called well founded magic sets techniques, tend to make too many magic facts true, which means that more calls are evaluated than necessary. A refinement is developed in [22] that generates fewer magic facts. The well founded magic sets ....

....search. Their technique, called Ordered Search, also maintains subgoal dependency information, and handles programs with left to right modularly stratified negation. For general programs, the magic sets transformation does not always preserve the well founded semantics [14] Methods proposed in [14, 15] to solve this problem, called well founded magic sets techniques, tend to make too many magic facts true, which means that more calls are evaluated than necessary. A refinement is developed in [22] that generates fewer magic facts. The well founded magic sets techniques use a doubled program, one ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic sets and bottom-up evaluation of well-founded models. In Intl. Logic Programming Symposium, pages 337--351, 1991.

No context found.

Kemp D. B., Stuckey P. J., and Srivastava D. Magic sets and bottom-up evaluation of wellfounded models. In Proceedings of the 1991.

....version has been operational since July 1989. From then on we have continuously enhanced the system, adding functionality and increasing performance. We also use Aditi as a research tool, as a platform on which to implement and evaluate new query evaluation algorithms and optimization techniques [1, 7, 9, 10, 11, 12, 13]. As of January 1993, interested researchers can obtain a beta test copy of Aditi under a nocost license. The distribution includes two text based interfaces that accept Aditi Prolog and SQL respectively, a graphical user interface, and a programming interface to NU Prolog. The distribution is in ....

....may include disjunction and negation. Like most deductive databases, Aditi currently supports only stratified forms of negation. However, this may change in the future, since we have developed a practical algorithm for computing answers to queries even in the presence of unstratified negation [10, 13]. This algorithm works on a magic transformed program where each predicate has two slightly different versions. At each iteration, the algorithm uses one set of versions to compute a set of definitely true facts, the other set to compute a set of possibly true facts. The next iteration can then ....

[Article contains additional citation context not shown here]

D. B. Kemp, P. J. Stuckey, and D. Srivastava. Magic sets and bottom-up evaluation of well-founded models. In Proceedings of the 1991 International Logic Programming Symposium, pages 337--351, San Diego, California, October 1991.

....defined only for definite programs. 1 Extending these strategies to normal logic programs would considerably improve their utility to deductive databases. For all such programs, the well founded semantics [16] is a three valued semantics that is widely accepted. Kemp, Srivastava and Stuckey [5] identified classes of programs and sips for which the magic sets transformation preserves well founded models with respect to the query. In this paper, we investigate other transformations that are based on propagating binding information using sips. Our contributions are: 1. We show that the ....

....transformation preserves well founded models with respect to the query for the same classes of programs and sips as does the magic sets transformation (Section 3) 2. We define a new program transformation based on magic sets and the doubled program approach for computing well founded models ([5]) that preserves well founded models with respect to the query for arbitrary sips applied to any program (Section 4) 1 Sagiv [11] also presented the envelopes transformation for stratified logic programs. 3. We extend the envelopes transformation to normal logic programs and show that it ....

[Article contains additional citation context not shown here]

Kemp, D.B., Srivastava, D. and Stuckey, P.J. Magic sets and bottom-up evaluation of well-founded models. In Proceedings of the Int. Logic Programming Symposium, San Diego (1991), 337--354.

....transformation of a modularly stratified program can lead to several problems. Firstly, it may be possible that the magic set transformed program does not agree with the query with respect to the well founded model of the program these problems are discussed for programs containing negation in [14, 15]. Secondly, even if query equivalence were preserved by a magic set transformation, the resulting program may not be a modularly stratified program. Indeed, the magic set transformation of an EMS program may not be an EMS program and we would not be able to use the evaluation techniques presented ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic sets and bottom-up evaluation of well-founded models. In Proceedings of the 1991 International Symposium on Logic Programming, pages 336--351, October 1991. An extended version, containing all proofs, is available as Melbourne University technical report 91/4.

No context found.

David Kemp, Divesh Srivastava, and Peter Stuckey. Magic sets and bottom-up evaluation of well-founded models. In Proceedings of the International Logic Programming Symposium, pages 337--351, San Diego, CA, U.S.A., October 1991.

....use O(m) space and make O(m) derivations in computing the query answer. For more details, see Example 3.2. We describe other top down and bottom up techniques that can evaluate left to right modularly stratified programs in Section 5. As an example, the doubled program technique of Kemp et al. [7] would also use O(m) space and make O(m) derivations on this example. However, if rule r1 were removed from P even , the doubled program approach would make O(m 2 ) derivations, though it would still use only O(m) space. Even on this modified program, Ordered Search would compute the answer to ....

....query evaluation techniques in the literature that compute answers under the well founded model. For example, WELL [2] is based on global SLS resolution; XOLDTNF [4] is an extension of OLDT resolution; GUUS [9] is based on the alternating fixpoint semantics; and the technique of Kemp et al. [7] is based on alternating fixpoint semantics and magic sets. The class of programs handled by these techniques is larger than that handled by Ordered Search, but each of these techniques can repeat computation even for left to right modularly stratified programs. This can result in a loss of ....

D. Kemp, D. Srivastava, and P. Stuckey. Magic sets and bottom-up evaluation of well-founded models. In Proceedings of the International Logic Programming Symposium, pages 337--351, San Diego, CA, U.S.A., Oct. 1991.

No context found.

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT, June 1991.

No context found.

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT, June 1991.

No context found.

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT, June 1991.

No context found.

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337--351. MIT, June 1991.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC