H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Kowalski and Bowen [10], pages 195--211.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....We can divide these methods in two groups. One idea is to perform a bottomup computation, but on a transformed program [1] The transformation depends on the query and introduces goal orientedness. One such method is known as Magic Templates [16] The other idea is to add so called tabulation [20] (memo ing [6] lemma resolution [21] to SLD resolution. In its simplest form, this involves storing intermediate results (lemmas) in a table, and looking up these tabled results instead of recomputing them. In this way, both the termination properties (the method is terminating for all deductive ....

....computation and magic bottom up computation. Moreover, it will facilitate the analysis of their behavior, in particular the prediction and explanation of their incompletenesses, if any. The plan of this paper is as follows. In Section 2 we give the traditional presentation of OLDT resolution [20], a specific variant of tabulated SLDresolution. In Section 3, we present the Magic Templates transformation and the related bottom up computation. We also give an alternative characterization of the resulting computation by what we call deduction sets : a set of statements is expanded until it ....

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H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Kowalski and Bowen [10], pages 195--211.

....inefficient, often solving previously solved goals over and over again. OLDT resolution, due to Tamaki and Sato [34] is a technique which caches previously derived solutions in a table. The theory and implementation of OLDT has been studied extensively by several researchers including Seki [28, 27] and Warren and his colleagues [9, 10] Furthermore, it is known that OLDT and magic set computations [5, 6, 26] are essentially equivalent, though they differ in many (relatively minor) details. We will use the OLDT technique as our starting point, and extend it as follows: 1) Multiple ....

H. Seki and H. Itoh. (1989) A Query Evaluation Method for Stratified Programs under the Extended CWA, Proc. 5th Intl. Conf./Symp. on Logic Programming (eds. K. Bowen and R. Kowalski), pps 195--211.

....it is unclear how often subgoal redundancies occur in real programs and the engine overhead needed to detect such situations would appear to be large 3 . An attractive alternate form of detecting these redundancies would be to use static analysis to approximate these situations. Seki and Itoh [63] and Kemp and Topor [36] extend OLDT and SLD AL respectively to stratified programs. 63] formalizes OLDTNF, which completely evaluates negative goals of lower strata before their use in higher strata. 36] proposes a similar extension of SLD AL using SLS resolution ( 49] The primary difference ....

....needed to detect such situations would appear to be large 3 . An attractive alternate form of detecting these redundancies would be to use static analysis to approximate these situations. Seki and Itoh [63] and Kemp and Topor [36] extend OLDT and SLD AL respectively to stratified programs. [63] formalizes OLDTNF, which completely evaluates negative goals of lower strata before their use in higher strata. 36] proposes a similar extension of SLD AL using SLS resolution ( 49] The primary difference between the two approaches is that OLDTNF assumes a fixed scheduling strategy, while ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Logic Programming: Proc. of the Fifth Int'l Conf. and Symp., pages 195--211, 1988.

.... directly by means of abduction [34, 6] ffl Tabling can be used as a means to aggregate solutions for annotation logics [74] 75] 89] 115] 41] 35] or preference logics [58] 29] 4 Overview ffl A (very partial ) bibliography Formulations of Tabling: 48] 19] 122] 46] 71] [112], 128] 132] 23] 40] 81] 123] 24] 21] 32] 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] ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In JICSLP, pages 195--211, 1988.

.... Allows logic programming systems to be used to explore Knowledge Representation. Tabling as defined below for WFS has polynomial data completity. 5 Motivation ffl There has been a lot 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 ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Logic Programming: Proc. of the Fifth Int'l Conf. and Symp., pages 195--211, 1988.

....one, instead of being solved using rules in a program, it is solved using answers computed for the previous subgoal. This avoids infinite branches and redundant computation due to repeated subgoals in the search space of SLD resolution. These techniques have been generalized to stratified programs [20, 40] and modularly stratified programs [37] Non termination may also occur due to infinite recursion through negation, which has to be treated differently from infinite recursion in definite programs. A positive loop, such as p p, is considered failed as can be seen in the well founded partial ....

....succeed or fail before the corresponding negative literal is solved by negative return. Thus the results in Section 5 can be specialized to locally stratified programs and the corresponding perfect Herbrand model. Extensions of OLDT [43] and SLD AL [49] have been developed for stratified programs [20, 40]. Our restriction of SLG resolution to locally stratified programs differs in that a single system of subgoals is maintained, which guarantees that each subgoal be evaluated only once. 6.3 Modularly Stratified Programs Ross [37] studied a more general class of programs that can be evaluated in a ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Joint Intl. Conference and Symposium on Logic Programming, pages 195--211, 1988.

....more generally, for modularly acyclic programs [25] global SLS resolution is effective. In the absence of function symbols, the Herbrand Base is finite, and so effective procedures exist. 5 For function free programs global SLS resolution may be made effective by using the memoing techniques of [10, 26] to prune positive loops, and by also pruning negative loops. Global SLS resolution (and hence the well founded semantics) captures the meaning of all well behaved programs in the sense that every program without infinite recursion through 5 A polynomial time algorithm for constructing the ....

Hirohisa Seki and Hidenori Itoh. A query evaluation method for stratified programs under the extended cwa. In Proc. Fifth International Conference and Symposium on Logic Programming, 1988.

.... This can be done by simple loop checking techniques, or by tabulation (also known as memo ization or lemma resolution) For locally stratified programs, loop checking was studied by Bol [24] Tabulation for stratified programs was studied by Kemp and Topor [81] for SLS resolution and Seki and Itoh [155] for SLDNF resolution. By definition, in this setting only positive loops have to be dealt with. So their approach can remain close to tabulation for positive programs, by maintaining a table for each stratum. Chen and Warren [37] added a tabulation mechanism to the form of SLS resolution proposed ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Kowalski and Bowen [84], pages 195--211.

....with computing sons of a node : A; if infinitely many answers for A are involved. A subject for future work is developing techniques to finitely represent (some) infinite pre failed trees, cross sections and sets of constraints in order to strengthen this approach. Methods of tabulation [ST86, SI88, BD93] and of finite representing of infinite sets of answers [CI93] are relevant here. 7.1 Proof of Theorem 7.5 We begin with a characterization of the well founded semantics. Then we prove lemmas that imply soundness, completeness and independence from the selection rule of SLSFA resolution (Theorem ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In R. A. Kowalski and Bowen K. A., editors, Proc. of the Fifth International Conference and Symposium on Logic Programming, pages 195--211. The MIT Press, 1988.

....to get more precise estimation of it. Apt and Bezem [1] studied the completeness of SLDNF resolution for the class of general programs, called acyclic programs or locally hierarchical programs, for which every SLDNF derivation terminates. In contrast, Kemp and Topor [10] and Seki and Itoh [17] considered the case where an SLDNF resolution may not terminate. Our work is also of this direction. Their procedures use lemmas, a set of proved atoms, to avoid infinite computations and are complete with respect to perfect models of allowed stratified databases. Although [17] lifted their ....

....and Seki and Itoh [17] considered the case where an SLDNF resolution may not terminate. Our work is also of this direction. Their procedures use lemmas, a set of proved atoms, to avoid infinite computations and are complete with respect to perfect models of allowed stratified databases. Although [17] lifted their completeness result to the class of stratified programs with the bounded term size property and the safeness condition for negation of Van Gelder [23] they did not present any other sufficient syntactic conditions for those than that of allowed stratified databases. On the other ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In R.A.Kowalski and K.A.Bowen, editors, Proc. of the Fifth International Conference on Logic Programming, pp. 195--211, 1988.

....with subsumption check will result in finite evaluation trees and therefore can be implemented as a complete and always terminating algorithm. This is the case, in particular, for function free programs, or more generally for programs with the so called bounded tree property (see [KT] and [SI]) Obviously, in general, no effective and always terminating implementation of SLS resolution (as well as of any other reasonably complete procedure, including SLD and SLDNF resolution) is possible. 3. When defining SLS resolution we were, as usual, concerned only with the properties of the ....

Seki, H. and Itoh, H., "A Query Evaluation Method for Stratified Programs under the Extended CWA", Proceedings Logic Programming Conference, Seattle, Wash. 1988, 195-211.

....In some situations, the locality of a computation rule conflicts with its safeness [8] avoiding the selection of nonground negative literals, if possible. We propose a solution for this problem, which is not dealt with in [7] nor in the two proposed tabulation mechanisms for stratified programs [12, 25]. 2 Preliminaries We use the standard logic programming terminology and definitions of [14] By programs we understand normal programs. We prefer to use the term positive programs instead of definite programs . Definition 2.1 Let P be a program and A an atom. Let H L 1 ; L n be a ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Kowalski and Bowen [13], pages 195--211.

....inefficient, often solving previously solved goals over and over again. OLDT resolution, due to Tamaki and Sato [33] is a technique which caches previously derived solutions in a table. The theory and implementation of OLDT has been studied extensively by several researchers including Seki [29, 28] and Warren and his colleagues [9, 10] Furthermore, it is known that OLDT and magic set computations [5, 6, 27] are essentially equivalent, though they differ in many (relatively minor) details. We will use the OLDT technique as our starting point, and extend it as follows: 1) Multiple ....

H. Seki and H. Itoh. (1989) A Query Evaluation Method for Stratified Programs under the Extended CWA, Proc. 5th Intl. Conf./Symp. on Logic Programming (eds. K. Bowen and R. Kowalski), pps 195--211.

....well founded model semantics suggests that SLS resolution can be considered as a theoretical construct, describing an ideal sound and complete query answering procedure for general logic programs under the wellfounded semantics. On the other hand, as it was the case with standard SLS resolution [KT88, SI88], the extended SLS resolution can be effectively implemented for large classes of programs, thus constituting a practical query answering mechanism. The details of such an effective procedure are beyond the scope of this paper, but, somewhat simplifying, one can say, that loop checking will be ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended cwa. In R. Kowalski and K. Bowen, editors, Proceedings of the Fifth Logic Programming Symposium, pages 195--211, Cambridge, Mass., 1988. Association for Logic Programming, MIT Press.

....in which finite numbers of computed answers are used. Such an approximation is called SLDFA resolution in [4] It is sound and complete for Clark completion semantics in 3 valued logic [7] Better approximations are a subject for future research. An obvious hint is to use methods of tabulation [17, 18] for finite representation of infinite trees and methods like those presented in [2] for finite representation of infinite sets of answers. This work shows that a rather natural generalization of the standard concept of a failed tree provides a sound and complete operational semantics for two ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Proc. of the Fifth International Conference and Symposium on Logic Programming, pages 195--211, 1988.

....methods, developed for logic programming, as inference mechanisms for non monotonic reasoning. The author has shown in [Prz89c, Prz89a] that the well founded semantics has a sound and complete procedural mechanism, called SLS resolution and work has already begun on its effective implementation [KT88, SI88, War89]. The most significant seems to be the work of D.S. Warren on the Extended Warren Abstract Machine (XWAM) and a Prolog interpreter which computes the well founded (or 3 valued stable) semantics of logic programs rather than the traditional Clark s predicate completion semantics (see [PW91] for ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended cwa. In R. Kowalski and K. Bowen, editors, Proceedings of the Fifth Logic Programming Symposium, pages 195--211, Cambridge, Mass., 1988. Association for Logic Programming, MIT Press.

....the termination properties of SLDNF resolution and to avoid redundant computation of subgoals. Several extensions of SLD resolution with memoing have been studied, including extension tables [12] OLDT resolution [36] and QSQR [41] These techniques have been generalized to stratified programs [16, 34] and modularly stratified programs [32] Example 1.1 Consider the following program: e(a; b) e(b; c) e(b; a) tc(X; Y ) e(X; Y ) tc(X; Y ) e(X; Z) tc(Z; Y ) The SLD tree for tc(a; V ) is infinite. Figure 1 shows the OLDT forest for the same goal, which is finite. Each subgoal has a ....

....for B contains any body literal. 2 For locally stratified programs, the extra overhead of delaying and simplification (negation failure L, negation success L, atom success L, atom failure L) can be avoided. Extensions of OLDT [36] and SLD AL [42] have been developed for stratified programs [16, 34]. Our restriction of SLG resolution to locally stratified programs differs from those approaches in that a single system (or table) of subgoals is maintained, which guarantees that each subgoal is evaluated only once. 6.3 Modularly Stratified Programs Ross [32] studied a more general class of ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended cwa. In Joint Intl. Conference and Symposium on Logic Programming, pages 195--211, 1988.

....by a previous one, it is solved using answers computed for the previous subgoal, instead of rules in a program. This avoids infinite branches and redundant computation due to repeated subgoals in the search space of SLD resolution. These techniques have been generalized to stratified programs [20, 40] and modularly stratified programs [37] Non termination may also occur due to infinite recursion through negation, which has to be treated differently from infinite recursion in definite programs. A positive loop, such as p p, is considered failed since p is false in the well founded partial ....

....succeed or fail before the corresponding negative literal is solved by negative return. Thus the results in Section 5 can be specialized to locally stratified programs and the corresponding perfect Herbrand model. Extensions of OLDT [43] and SLD AL [49] have been developed for stratified programs [20, 40]. Our restriction of SLG resolution to locally stratified programs differs in that a single system (or table) of subgoals is maintained, which guarantees that each subgoal be evaluated only once. 6.3 Modularly Stratified Programs Ross [37] studied a more general class of programs that can be ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended CWA. In Joint Intl. Conference and Symposium on Logic Programming, pages 195--211, 1988.

....systems in table 2 XSB s evaluation method is SLG resolution, described in section 3. For definite programs, SLG is closely related to both OLDT [24] and to Extension Tables [8] However, these evaluation methods do not address negation, while other extensions of memoing approaches, such as [9] [20] differ significantly from SLG even for stratified programs. Most of the systems in table 2 use an extension of the magic set approach. 19] provides a one 1 A program flounders if there is an atom whose truth cannot be proven without making a call to a non ground negative literal. 2 ....

H. Seki and H. Itoh. A query evaluation method for stratified programs under the extended cwa. In Logic Programming: Proceedings of the Fifth International Conference and Symposium, pages 195--211, 1988.

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