K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Standford University, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....suspended or not. LRD stratified programs and their evaluation method are explained in detail in [28, 23] However, the following simple program is LRD stratified, but does not fit into other stratification classes (e.g. the more familiar class of (left to right) modularly stratified programs [25]. p: q, r, s. q: r, p. r: p, q. s: p, q, r. Before leaving the subject of stratification, we note that the use of completion also forms the basis of evaluation of programs with stratified findall 3 (See the description of predicate tfindall 3 on page 73) 5.2.1 Dynamic ....

K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, 1991.

....stable model of a logic program [13, 27, 33] Thus to derive true false answers that are specific to certain stable models, we have to focus only on atoms that are undefined in the well founded partial model. For logic programs without loops through negation, e.g. modularly stratified programs [31], the well founded partial model is total and coincides with the unique stable model of the program. In that case, computation of the well founded semantics is sufficient. Undefined atoms are involved in loops through negation. We discuss how negative loops should be handled in order to facilitate ....

K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, August 1991.

....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 model of p p where p is false. In ....

....to subgoals maintained in OLDT resolution [43] For definite programs, it has been shown [8, 39] that the top down with memoing and the set at a time approaches are essentially equivalent. Methods of query processing 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 ....

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K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, August 1991.

....suspended or not. LRD stratified programs and their evaluation method are explained in detail in [20, 16] However, the following simple program is LRD stratified, but does not fit into other stratification classes (e.g. the more familiar class of (left to right) modularly stratified programs [18]. p: q, r, s. q: r, p. r: p, q. s: p, q, r. Before leaving the subject of stratification, we note that the use of completion also forms the basis of evaluation of programs with stratified findall 3 2.3 Dynamic Stratification A simple rearrangement of the program of the previous section ....

K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, 1991.

....to capture relevant subgoals in a top down fashion by controlling the availability of magic tuples (that represent calls in a top down computation) This is achieved by maintaining subgoal dependencies in a sequence of so called ContextNodes. The idea of subgoal dependencies can be traced back to [21], where they were used to determine if subgoals were completely evaluated. However, the issue of efficient dependency maintenance was not investigated in detail. Our work on effective computation of the well founded semantics started with XOLDTNF [8] As we have mentioned, XOLDTNF uses a fixpoint ....

....B 0 must have been returned to G. By Definition 2.5, Scc are completely evaluated. By completion transformation, subgoals in Scc are popped off the stack and are marked as completed. 2 5 Related Work Ross first used subgoal dependencies in query evaluation with modularly stratified programs [21]. Facts representing (transitive) dependencies among subgoals are computed explicitly. However, techniques for efficient maintenance and computation of subgoal dependencies were not explored. The work most closely related to ours is the Ordered Search technique for bottom up evaluation of ....

Ross, K.A. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, August 1991.

....component C is a component such that if C contains a recursive predicate p, C contains all predicates on all paths from p to itself. Given a recursive component C, if there is a path from a predicate p to a predicate r, but C does not contain r, then r is used by C. Modularly stratified programs[6] are defined as a refinement of stratified and of locally stratified programs. Definition 2.13 (Modular Stratification[6] Let P be a program and OE be the partial ordering over recursive components of P . P is modularly stratified if, for every recursive component F of P , ffl There is a total ....

....p to itself. Given a recursive component C, if there is a path from a predicate p to a predicate r, but C does not contain r, then r is used by C. Modularly stratified programs[6] are defined as a refinement of stratified and of locally stratified programs. Definition 2. 13 (Modular Stratification[6]) Let P be a program and OE be the partial ordering over recursive components of P . P is modularly stratified if, for every recursive component F of P , ffl There is a total well founded model M for the union of all components F 0 OE F , and ffl The quotient of F modulo M , F M , is ....

[Article contains additional citation context not shown here]

K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, 1991.

....to capture relevant subgoals in a top down fashion by controlling the availability of magic tuples (that represent calls in a top down computation) This is achieved by maintaining subgoal dependencies in a sequence of so called ContextNodes. The idea of subgoal dependencies can be traced back to [21], where they were used to determine if subgoals were completely evaluated. However, the issue of efficient dependency maintenance was not investigated in detail. Our work on effective computation of the well founded semantics started with XOLDTNF [5] As we have mentioned, XOLDTNF uses a fixpoint ....

.... magic tuples: mp(a) mp(b1) mp(bn) mp(c1) mp(cn 1) Our implementation of SLG resolution generates only subgoals (or magic tuples) that are relevant, namely p(a) p(b1) p(c1) p(b2) p(c2) Ross first used subgoal dependencies in query evaluation with modularly stratified programs [21]. Facts representing transitive dependencies among subgoals are 34 computed explicitly. However, techniques for efficient maintenance and computation of subgoal dependencies were not explored. The work most closely related to ours is the Ordered Search technique for bottomup evaluation of ....

Ross, K.A. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, August 1991.

....stable models. This section shows how to integrate computations of the well founded semantics and stable models to provide query evaluation of non ground programs for practical applications. It is known that for logic programs without loops through negation, e.g. modularly stratified programs [25], the well founded partial model is total and coincides with the unique stable model of the program. In that case, computation of the well founded semantics is sufficient. For programs with literals involved in loops through negation, the well founded partial model is in general three valued. We ....

K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, August 1991.

....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 corresponding OLDT tree. A node in an ....

....to subgoals that are maintained in OLDT resolution. For definite programs, it has been shown [8, 33] that the top down with memoing and the set at a time approach are essentially equivalent. Methods of query processing 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 ....

[Article contains additional citation context not shown here]

K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, August 1991.

....avoid unnecessary computation caused by treating them as undefined. As a special case of the above, for modularly stratified programs WF OS reduces to Ordered Search, and performs no irrelevant computation and repeats no computation. Our technique is better than WELL [7] and QSQR SLS resolution [22] since both perform repeated computation even for programs without negation. Unlike XOLDTNF [9] our technique is able to share answers to subgoals effectively; XOLDTNF repeats computation even for modularly stratified programs. The technique of [13] is not goal directed, although they mention that ....

Kenneth A. Ross. The Semantics of Deductive Databases. Ph.D. thesis, Department of Computer Science, Stanford University, Aug. 1991.

....run time information about the truth value of atoms is central to whether the derivation path remains suspended or not. The following simple program is LRD stratified, but does not fit into other stratification classes (e.g. the more familiar class of (left to right) modularly stratified programs [17]) p q, r, s q r, p r p, q s :p, q, r Before leaving the subject of stratification, we note that the use of completion also forms the basis of evaluation of programs with stratified uses of aggregation. 2.3 Dynamically Stratified Negation A simple rearrangement of the program ....

....Consider the program p :s, r, q q r, p r p, q s :p, q, r which cannot be evaluated by the method sketched above. However, the wellfounded model of this program is total. Such programs, are called dynamically stratified, but may not be stratified for any particular evaluation order [15, 17]. 3 This use of completion allows ground queries to Datalog programs with negation to be computed with polynomial data complexity. XSB handles dynamically stratified programs through delaying of negative literals when it becomes necessary to look to their right in a clause, and then ....

K. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, 1991.

....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 model of p p. In contrast, a negative ....

....correspond to subgoals maintained in OLDT resolution [43] For definite programs, it has been shown [8, 39] that the top down with memoing and the set at a time approach are essentially equivalent. Methods of query processing 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 ....

[Article contains additional citation context not shown here]

K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Department of Computer Science, Stanford University, August 1991.

....domains. We can slightly modify our condition of universal constraint stratification to require that all cycles, not just those having at least one negative edge, have unsatisfiable constraints. With that extension we get a condition analogous to acyclicity [AB90] or modular acyclicity [Ros91]. Programs satisfying these conditions have good termination properties: they can be evaluated either top down without memoing, or bottom up without duplicate elimination. In general, both top down methods without memoing and bottomup methods without duplicate elimination can get trapped in ....

K. A. Ross. The Semantics of Deductive Databases. PhD thesis, Stanford University, August 1991. Stanford University Technical Report STAN-CS-91-1386.

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K.A. Ross. The Semantics of Deductive Databases. PhD thesis, Standford University, 1991.

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