D. Kemp, P. Stuckey, and D. Srivastava. Query Restricted Bottom-up Evaluation of Normal Logic Programs. In Proc. of ICLP, pages 288-302. MIT Press, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....method (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 ....

D. Kemp, P. Stuckey, and D. Srivastava. Query Restricted Bottom-up Evaluation of Normal Logic Programs. In Proc. of ICLP, pages 288-302. MIT Press, 1992.

....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 decreasing, but are computed in an ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Query restricted bottom-up evaluation of normal logic programs. In Joint Intl. Conference and Symposium on Logic Programming, pages 288--302, 1992.

....semantic proposals were set forth from the late eigthies onwards including the well founded semantics (WFS) of [12] which deals semantically with non terminating computations, and thereby giving semantics to every program. For this semantics several query evaluation procedures have been defined [3, 5, 7, 14, 18, 20, 21, 23, 24]. In recent years several authors (e.g. 13, 19, 26] have shown the importance of extending LP with a second kind of negation : for use in deductive databases, knowledge representation, and non monotonic reasoning (NMR) Different semantics for extended LPs with : negation (ELP) have appeared ....

D. B. Kemp, P. J. Stuckey, and D. Srivastava, `Query Restricted Bottom-up Evaluation of Normal Logic Programs', in Proc. JICSLP'92, pp. 288--302. MIT Press, (1992).

....semantics (WFS) of [24] which deals semantically with non terminating topdown computations, by assigning such computations the truth value of false or undefined , and thereby giving semantics to every program. For this semantics several query evaluation procedures have been defined [7, 11, 13, 32, 47, 53, 54, 57, 61]. The well founded semantics deals only with normal programs, i.e. those with just negation by default, and thus it provides no mechanism for explicitly declaring the falsity of literals. This can be a serious limitation. The evolution of Logic Programming (LP) semantics has now included the ....

D. B. Kemp, P. J. Stuckey, and D. Srivastava. Query Restricted Bottom--up Evaluation of Normal Logic Programs. In Proc. JICSLP'92, pages 288--302. MIT Press, 1992.

....information from the query into the rule evaluation so that only information relevant to the query is accessed. Various authors have looked at the problem of extending the magic sets techniques to larger classes of programs with negation, be it stratified, modularly stratified, or general negation [Ros90, RSS92, Mor93, KSS92]. In general, the larger the class of programs allowed, the fewer options there are for optimization, and so we look for the most specific optimization technique that applies. As an obvious example, one would not use any of the techniques for magic set with negation on a program without ....

D. Kemp, P. Stuckey, and D. Srivastava. Query restricted bottom-up evaluation of normal logic programs. In Proc. Joint International Conference and Symposium on Logic Programming, pages 288--302, 1992.

....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 forest of Bol ....

....and therefore made it possible to use the notion of u assumption and abortion of unsound branches instead. If negative literals are always delayed in SLG resolution it seems to correspond to complete search in the search forest when u assumptions are made blindly. Kemp, Stuckey and Srivastava [KSS92] have a similar approach to ours but intertwine the magic transformation and the fixed point computation whereas our approach separates the two. In addition their approach seems to presuppose a particular fixed point characterization. The transformation described here is independent of any such ....

D. Kemp, P. Stuckey, and D. Srivastava. Query Restricted Bottom-up Evaluation of Normal Logic Programs. In K. Apt, editor, Proc. of Joint International Conf. and Symp. on Logic Programming, Washington, pages 288--302. The MIT Press, 1992.

....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. Query restricted bottom-up evaluation of normal logic programs. In Joint Intl. Conference and Symposium on Logic Programming, pages 288--302, 1992.

....one would need a more general, nonsequential method for maintaining negative dependencies, that would be less efficient in general. For a detailed discussion of this point on normal programs, see [16] Subsequent to [16] several other magic set procedures have been proposed for normal programs [7, 9, 15]. Extending these techniques to HiLog programs is an interesting direction for future research. While the transformation of [16] is well defined for all range restricted, modularly stratified normal programs, the evaluation of the transformed program is not guaranteed to terminate for programs ....

D. Kemp, P. Stuckey, and D. Srivastava. Query restricted bottom-up evaluation of normal logic programs. In Proc. Joint International Conference and Symposium on Logic Programming, pages 288--302, 1992.

....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. Query restricted bottom-up evaluation of normal logic programs. In Joint Intl. Conference and Symposium on Logic Programming, pages 288--302, 1992.

....the well founded semantics (WFS) of [27] which deals semantically with non terminating computations by assigning such computations the truth value of false or undefined , and thereby giving semantics to every program. For this semantics several query evaluation procedures have been defined [7, 11, 13, 35, 51, 58, 59, 62, 66]. The well founded semantics deals with normal programs, i.e. those with only negation by default, and thus it provides no mechanism for explicitly declaring the falsity of literals. This can be a serious limitation. The evolution of Logic Programming semantics has included the introduction of a ....

D. B. Kemp, P. J. Stuckey, and D. Srivastava. Query Restricted Bottom--up Evaluation of Normal Logic Programs. In Proc. JICSLP'92, pages 288--302. MIT Press, 1992.

....that the predicate is an extensional database (EDB) predicate; otherwise the predicate is an intensional database (IDB) predicate. We consider only Horn programs in this paper. The techniques developed in this paper could be extended to programs with negation by combining with the techniques of [9, 12, 17, 19]. HiLog It will be convenient in our exposition to use HiLog notation for some meta predicates [5] HiLog allows one to have atoms as terms in other atoms. For example, we might write magic(h(X) where h is a predicate symbol rather than a function symbol. The use of HiLog in the present ....

Kemp, D., Stuckey, P., and Srivastava, D. Query restricted bottom-up evaluation of normal logic programs. In Proc. Joint International Conference and Symposium on Logic Programming (1992), MIT Press, Cambridge, Massachusetts, pp. 288--302.

....including the well founded semantics (WFS) of [12] which deals semantically with non terminating computations, by assigning such computations the truth value undefined , and thereby giving semantics to every program. For this semantics several query evaluation procedures have been defined [2, 4, 6, 15, 19, 22, 23, 26, 27]. In recent years several authors (e.g. 13, 20, 29] have stressed the importance of extending LP with a second kind of negation : for use in deductive databases, knowledge representation, and non monotonic reasoning (NMR) Different semantics for extended LPs with : negation (ELP) have ....

....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 extensions. In spite of not treating positive recursion and non cyclic negative recursion, it has several similarities with our method. The abductive ....

D. B. Kemp, P. J. Stuckey, and D. Srivastava. Query Restricted Bottom--up Evaluation of Normal Logic Programs. In Proc. JICSLP'92, pages 288--302. MIT Press, 1992.

....have been investigated for stratified and modularly stratified programs [3, 29, 32] With negation, the major issue becomes maintaining dependencies among magic tuples (or subgoals) so as to ensure that a positive subgoal is fully evaluated before its negative counterpart is resolved. Kemp et al. [15] developed a technique that computes the well founded semantics using a double program, one for deriving definitely true and false answers and the other for deriving possibly true or false answers. However, it makes too many magic facts true, which means that more subgoals are evaluated than ....

....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. Query restricted bottom-up evaluation of normal logic programs. In Joint Intl. Conference and Symposium on Logic Programming, pages 288--302, 1992.

....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 decreasing, but are computed in an ....

David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Query restricted bottom-up evaluation of normal logic programs. In Joint Intl. Conference and Symposium on Logic Programming, pages 288--302, 1992.

....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 ....

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D. Kemp, P. Stuckey, and D. Srivastava. Query restricted bottom-up evaluation of normal logic programs. In Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 288--302, Washington DC, November 1992.

....programs without negation, several memoing evaluation techniques have been proposed [2, 17, 24, 27] Several attempts have been made at extending some of these for computing the well founded semantics. These past attempts have the problem that either the computation is not completely goaldirected [13, 11, 12, 15] since some facts that are irrelevant to the computation may be generated, or compute only relevant facts, but may compute some of them multiple times [9] We present more details on related work in Section 7. But, in particular, for the important special case of modularly stratified programs ....

....query by calculating the set of queries that the original query depends on . They were originally defined only for positive programs, and most such transformations are incorrect when applied to programs with negation since their notion of depends on is not applicable if negation is used (see [12]) We provide some background on bottom up evaluation using the Magic Templates transformation. The bottom up approach to answering queries consists of a two part process. First, the programquery pair is rewritten in a form so that the bottom up fixpoint evaluation of the program will be more ....

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David Kemp, Divesh Srivastava, and Peter Stuckey. Query restricted bottom-up evaluation of normal logic programs. In Procs. of the Joint Int'l Conf. and Symp. on Logic Programming, 288-- 302, 1992.

....transformation does not always preserve the answers of the query [16] For restricted classes of programs and sips the transformation is answer preserving for DATALOG : and the same results apply to constraint logic programs. We can similarly extend the well founded magic sets approaches of [17, 24] to constraint logic programs to enable us to evaluate arbitrary sip allowed programs P for arbitrary (allowed) sips strategies S in a query directed manner. Given an arbitrary constraint program P , if we can determine the finiteness dependencies for the constraints of each rule in P then we can ....

....; S ; Q) then call P A Q S def = fp( x) j magic p( x ) 2 gfp(F 2 MP )g We must ensure that adding constraints that hold of all calling patterns to the rules of the original program does not change the answers of the program with respect to the queries. We can use the following result of [17] which shows that as long as we consider the true and undefined atoms in the magic templates (gfp(F 2 MP ) the well founded model of P restricted to the queries only depends on the atoms covered by calling patterns. Proposition 2 [17] Let P be a program and S a sip strategy and Q a set of ....

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D.B. Kemp, D. Srivastava, and P.J. Stuckey. Query Restricted Bottom-up Evaluation of Normal Logic Programs. Proceedings of the Joint Int. Conf. and Symp. on Logic Programming, Washington (1992), 288--302.

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