C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: The LDL++ Approach. In Proc. 3rd Int. Conf. on Deductive and Object-Oriented Databases (DOOD93), volume 760 of Lecture Notes in Computer Science, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....mechanisms supporting: temporal reasoning, by means of temporal, or stage, arguments of relations, ranging over a discrete temporal domain, in the style of Datalog 1S [5] nonmonotonic reasoning, by means of a form of strati ed negation w.r.t. the stage arguments, called XY strati cation [19]; nondeterministic reasoning, by means of the nondeterministic choice construct [8] Datalog , which is essentially a fragment of LDL [2] and is advocated in [20, Chap. 10] revealed a highly expressive language, with applications in diverse areas such as AI planning [4] active rules ....

....atoms, thus bounding the scope of the atom to the rule it appears in. The various stable models of the transformed program SV (P ) thus correspond to the choice models of the original program. XY programs. Another notion used in this paper is that of XY programs originally introduced in [19]. The language of such programs is Datalog : 1S , which admits negation on body atoms and a unary constructor symbol, used to represent a temporal argument usually called the stage argument. A general de nition of XY programs is the following. A set P of rules de ning mutually recursive ....

[Article contains additional citation context not shown here]

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: The LDL++ Approach. In Proc. 3rd Int. Conf. on Deductive and Object-Oriented Databases (DOOD93), volume 760 of Lecture Notes in Computer Science, 1993.

....supporting: a limited form of temporal reasoning, by means of temporal, or stage, arguments of relations, ranging over a discrete temporal domain, in the style of [5] nonmonotonic reasoning, by means of a form of stratified negation w.r.t. the stage arguments, called XY stratification [26]; nondeterministic reasoning, by means of the nondeterministic choice construct [12] Datalog , which is essentially a fragment of LDL [2] and is advocated in [27, Chap. 10] revealed a highly expressive language, with applications in diverse areas such as AI planning [4] active ....

....the total sum is reconstructed from sum r(X; N) when X is the last tuple in the order. Notice the use of (stratified) negation to the purpose of selecting the last tuple. In practical languages, such as LDL , some syntactic sugar for aggregation is used as an abbreviation of the above program [26]: total sum r(sum X ) r(X) On the basis of this simple example, more sophisticated forms of aggregation, such as datacube and other OLAP functions, can be built. As an example, consider a relation sales(Date, Department, Sale) and the problem of aggregating sales along the dimensions Date ....

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C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: The LDL++ Approach. In Proc. 3rd Int. Conf. on Deductive and Object-Oriented Databases (DOOD93), volume 760 of Lecture Notes in Computer Science, 1993.

....section we discuss related research results as well as possible future extensions of the proposed technique. Related Work: During the time that this paper was under review, the author became aware of two other approaches for adding negation to temporal logic programming, namely XY stratification [ZAO93] and state stratification [Lud98] Both approaches however apply to temporal languages that have a rather restricted syntax, and are therefore in this respect less general than the cycle sum approach introduced in this paper. The XY stratification approach was developed for the language ....

....and state stratification [Lud98] Both approaches however apply to temporal languages that have a rather restricted syntax, and are therefore in this respect less general than the cycle sum approach introduced in this paper. The XY stratification approach was developed for the language XY Datalog [ZAO93], which has been proposed as a formalism for combining active and deductive rules. In XYDatalog, rules have a distinguished first argument (the stage argument) which represents the notion of time. A stage argument can have three possible values, namely nil, I and s(I) The notion of ....

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C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: the LDL++ Approach. In Proceedings of DOOD-93, December 6-8 1993. Phoenix, Arizona, USA. 13

....Computing WFS via States. The sequence of applications of Gamma P can be computed by a logic program which is obtained from the original program by introducing an additional argument position for IDB relations, representing the state sequence (this construction is a variant of [KRS95] see also [ZAO93] LHL95] Corresponding to the definition of T J P , in each rule, this argument is set to S 1 for all positive literals (including the head literal) otherwise to S. The distinguished state variable S is restricted by the additional literal state(S) The rule from Example 1 translates into ....

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: the LDL++ Approach. In Ceri et al. [CTT93].

....events here, although several of these like conjunction, disjunction, negation and sequence can be defined by means of Statelog rules. 4 Yet another solution is to choose non deterministically one rule order or one single rule. This can be accomplished using a nondeterministic choice construct [34], however we do not elaborate on this in the present paper. 4 A more general solution is to use integrity constraints expressing the desired functional dependencies. It is well known that any first order definable integrity constraint can be coded into a deductive rule in the form of a denial . ....

....This ensures that running is true iff there are changes in Delta relations which in turn guarantees that all relations with an unconditioned frame rule like (4.1) are constant during the running phase of a transaction. 5 Related Work The idea of using state terms in Datalog has been proposed in [33, 34] to allow a unified semantics for active and deductive rules, and independently in [21, 22] as a means to specify update procedures in a declarative way. X and Y rules of [33] are very similar to local and progressive rules, respectively. However, while local and progressive rules may involve ....

[Article contains additional citation context not shown here]

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: the LDL++ Approach. In S. Ceri, K. Tanaka, and S. Tsur, editors, Proc. Intl. Conference on Deductive and Object-Oriented Databases (DOOD), number 760 in LNCS. Springer, 1993. 17

....computation path beginning in g 0 in the minimal Kripke Model K. Thus, the logic programming semantics is also adequate w.r.t. the intuitive semantics. 7 Related Work The idea of using state terms to refer to different states in logical rules has come up several times, e.g. in XY Datalog [Zan93, ZAO93] to allow a unified semantics for active and deductive rules, and in [KLS92, LL94] as a means to specify updates in a declarative way. Flat Statelog [LHL95] XY Datalog, and the temporal query languages Datalog 1S and Templog [Cho90, AM89, Bau95] are closely related, since they all extend ....

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: the LDL + + Approach. In S. Ceri, K. Tanaka, and S. Tsur, eds., DOOD, Springer LNCS 760, 1993. 20

.... mechanisms, the deductive query processing, the semantics of active rules, and the integration of these various competing paradigms in a coherent framework from this point of view, it is helpful that the semantics of the adopted fragment of LDL is assigned in purely declarative terms [SZ90, ZAO93]. On the other side, the proposed compilation is low level enough to form the basis of a realistic (prototype) implementation, as LDL can be efficiently executed by means of a fixpoint procedure with real side effects to support updates. The static component of the considered object model, ....

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: The LDL++ Approach. In Int. Conf. on Deductive and Object-Oriented Databases, DOOD'93, 1993.

....control of the fixpoint computation can be expressed declaratively as well. The device of stage parameter can be used to express other aspects of control as well. Originally it had been introduced in the context of the counting method [SZ87] In a new paper, to be presented at DOOD 93 as well [ZAO93], XY stratification is proposed. For this class of rules, stage parameters can be used for making stratification layers explicit, thus enabling an ordinary fixpoint procedure to even handle certain locally stratified rule sets the processing of which normally requires the use of an iterated ....

C. Zaniolo, N. Arni, and K. Ong: "Negation and Aggregates in Recursive Rules: the LDL++ Approach", in: Proc. DOOD93

....mechanisms supporting: temporal reasoning, by means of temporal, or stage, arguments of relations, ranging over a discrete temporal domain, in the style of Datalog 1S [5] nonmonotonic reasoning, by means of a form of stratified negation w.r.t. the stage arguments, called XY stratification [19]; nondeterministic reasoning, by means of the nondeterministic choice construct [8] Datalog , which is essentially a fragment of LDL [2] and is advocated in [20, Chap. 10] revealed a highly expressive language, with applications in diverse areas such as AI planning [4] active rules ....

....atoms, thus bounding the scope of the atom to the rule it appears in. The various stable models of the transformed program SV (P ) thus correspond to the choice models of the original program. XY programs. Another notion used in this paper is that of XY programs originally introduced in [19]. The language of such programs is Datalog : 1S , which admits negation on body atoms and a unary constructor symbol, used to represent a temporal argument usually called the stage argument. A general definition of XY programs is the following. A set P of rules defining mutually recursive ....

[Article contains additional citation context not shown here]

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: The LDL++ Approach. In Proc. 3rd Int. Conf. on Deductive and Object-Oriented Databases (DOOD93), volume 760 of Lecture Notes in Computer Science, 1993.

....by selecting the following mechanisms: Re: i) predicates may have a distinguished temporal, or stage argument, ranging over a discrete temporal domain, in the style of Datalog 1S [8] Re: ii) a form of stratified negation w.r.t. the stage arguments is adopted, called XY stratification [23]; Re: iii) the non deterministic choice construct of deductive databases is adopted [12] This logic database language, which is essentially a fragment of LDL [4] is the object of study of this paper, and is referred to with the name Datalog . Although Datalog reveals a highly ....

....ones via diffchoice r , so that in each stable model of SV (P ) there is (only) one of them. The various stable models of the transformed program SV (P ) thus correspond to the choice models of the original program. Another notion used in this paper is that of XY programs originally introduced in [23]. The language of such programs is Datalog : 1S , which admits negation on body atoms and a unary constructor symbol, used to represent a temporal argument usually called the stage argument. A general definition of XY programs is the following. A set P of rules defining mutually recursive ....

[Article contains additional citation context not shown here]

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: The LDL++ Approach. In Int. Conf. on Deductive and Object-Oriented Databases, DOOD'93, 1993.

....support the choice construct for non deterministic programming and the concept of XY stratification that allows for negation and set aggregates in recursive rules. The formal semantics of both constructs is based on stable models. Because of limited space, we will not discuss XY stratification [21], and concentrate instead on the non deterministic choice construct. The idea of choice was introduced in [8] to express non determinism in a declarative fashion. Thus, a construct such as choice( X) Y) is used to denote that the functional dependency X Y must hold in the model defining ....

....operational semantics based on the notion of memorizing the old values of choice and checking every candidate new value for violations of the FD constraints. This operational semantics is also the basis for efficient implementations of the construct. Likewise, the notion of XY stratification [21] a combination of formal non monotonic semantics, intuitive appeal and amenability to efficient implementations are the ingredients that allow the relaxation of the stratification requirement in LDL . 4 Conclusions and Future Directions The realization of the LDL prototype, a second generation ....

Zaniolo, C., N. Arni, and K. Ong, "Negation and Aggregates in Recursive Rules: the LDL++ Approach," Procs. Third Int. Conference on Deductive and Object-Oriented Databases, Dec. 6-8, 1993, Scottsdale, Arizona.

....strategy like forward or backward chaining. 1 On the other hand, the use of state terms extends the expressiveness and control capabilities of the language which are necessary to describe active data manipulation operations. The idea of using state terms in Datalog has been proposed in [26, 27] to allow a unified semantics for active and deductive rules, and independently in [15, 16] as a means to specify update procedures in a declarative way. The main contributions of this paper are as follows. We demonstrate that the proposed language Statelog can afford both active rules and ....

....closure by adding new edges only at state transitions instead of using a single state. tation with relative ease, their theoretical implications remain an interesting field of future research. One possibility e.g. is to allow nondeterministic extensions (like invented values or choice, see e.g. [27]) which are a powerful programming tool and have a similar impact on expressiveness like assuming an ordered database. ....

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: the LDL++ Approach. In S. Ceri, K. Tanaka, and S. Tsur, editors, Proc. Intl. Conference on Deductive and Object-Oriented Databases (DOOD), number 760 in LNCS. Springer, 1993.

....the bistate version of P and is denoted P bis . Example 7 The bistate version of the program in Example 6 new delta anc(marc) new delta anc(Y) # old delta anc(X) parent(Y, X) old all anc(Y) new all anc(X) # new delta anc(X) new all anc(X) # old all anc(X) Now we have that [55, 57]: Definition 3 Let P be an XY program. P is said to be XY stratified when P bis is a stratified program. Theorem 3 Let P be an XY stratified program. Then P is locally stratified. The program of Example 7 is stratified with the following strata: S 0 = parent, old all anc, old delta anc , S 1 ....

....S 0 = parent, old all anc, old delta anc , S 1 = new delta anc , and S 2 = new all anc . Thus, the program in Example 6 is locally stratified. For an XY stratified program P , the general iterated fixpoint procedure [32] used to compute the stable model of locally stratified programs [55] becomes quite simple; basically it reduces to a repeated computation over the stratified program P bis . For instance, for Example 7 we compute new delta anc from old delta anc and then new all anc from this. Then, the old relations are re initialized with the content of the new ones so ....

Zaniolo C., Arni N. and Ong, KayLiang, "Negation and Aggregates in Recursive Rules: the LDL++ Approach," Procs. Third Int. Conference on Deductive and ObjectOriented Databases, Dec. 6-8, 1993, Scottsdale, Arizona.

....the only alternative since many existing deductive database systems provide the user with enough control to implement this, and other di#erential improvements previously discussed, by coding them into the program. For instance, the LDL users could use XY stratified programs for this purpose [28]; similar programs can be used in other systems [25] 8 Conclusion This paper has introduced a logic based approach for the design and implementation of greedy algorithms. In a nutshell, our design approach is as follows: i) formulate the all answer solution for the problem at hand (e.g. find ....

Zaniolo, C., N. Arni, K. Ong, Negation and Aggregates in Recursive Rules: the LDL++ Approach, Proc. 3rd DOOD Conference, 1993.

....and Ullman 1995) provide support for modular stratification (Ross 1994) which is more powerful than stratification but fail to solve the usability issue. On the other hand, the notion of XY stratification supported in LDL solves both the issue of expressive power and that of usability (Zaniolo et al. 1993). A second line of attack, rather than attempting to solve the nonmonotonicity conundrum, tries to circumvent it by observing that in many applications of interest, e.g. greedy algorithms (Ganguly et al. 1995) aggregates are used in a monotonic way. This idea of monotone aggregation was ....

....is called the bistate version of P and is denoted P bis . Example 7 The bistate version of the program in Example 6 new delta anc(marc) new delta anc(Y) old delta anc(X) parent(Y; X) old all anc(Y) new all anc(X) new delta anc(X) new all anc(X) old all anc(X) Now we have that (Zaniolo et al. 1993, Zaniolo et al. 1997) Definition 3 Let P be an XY program. P is said to be XY stratified when P bis is a stratified program. Theorem 3 Let P be an XY stratified program. Then P is locally stratified. The program of Example 7 is stratified with the following strata: S 0 = fparent; old all anc; ....

[Article contains additional citation context not shown here]

Zaniolo, C., Arni, N. Ong, K. (1993). Negation and Aggregates in Recursive Rules: the LDL++ Approach. DOOD'93, S. Ceri, K. Tanaka, S. Tsur (Eds.), pp. 204--221, Springer, 1993.

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Carlo Zaniolo, N. Arni, and K. Ong. "Negation and Aggregates in Recursive Rules: the LDL++ Approach." DOOD, 1993.

....developed in one framework to the others. For instance, since the experience of SQL, QBE and QUEL has well demonstrated that set aggregates should be included as primitive in a query language, one of the first tasks undertaken by the designers of LDL was extending Datalog with set aggregates [ZAO93]. Conversely, the experience gained with recursive queries in Datalog has recently resulted in the introduction of new recursive query constructs for SQL [FMM96] TSQL2 offers no hope for such cross fertilization because its new temporal constructs, restructuring, partitioning, etc. are totally ....

C. Zaniolo, N. Arni and K. Ong. Negation and Aggregates in Recursive Rules: the LDL++ Approach. In Proceedings of the 3rd International Conference on Deductive and Object-Oriented Databases, pages 204-221, 1993

No context found.

Carlo Zaniolo, N. Arni, and K. Ong. "Negation and Aggregates in Recursive Rules: the LDL++ Approach." DOOD, 1993.

....of priorities to rules (or the validation of priorities assigned by the programmer) and (3) generalized termination policies. In my recent research, I have been pursuing the thesis that a conceptual unity underlies the areas of active databases, temporal databases and deductive databases [13, 14, 11]. The results of this paper bring further support to this thesis, and, hopefully, will promote the confluence of these three areas of database research. Acknowledgments Thanks are due to the referees and Antonio Brogi for many improvements. ....

Zaniolo, C., N. Arni, K. Ong, "Negation and Aggregates in Recursive Rules: the LDL++ Approach", Proc. 3rd Int. Conf. on Deductive and O-O DBs, DOOD-93, Phoenix, AZ, Dec 6-8, 1993.

No context found.

Zaniolo, C., N. Arni, K. Ong, "Negation and Aggregates in Recursive Rules: the LDL++ Approach", Proc. 3rd Int. Conference on Deductive and O-O DBs, DOOD-93, Phoenix, AZ, Dec 6-8, 1993.

....part subpart graph; but, in SQL3, all queries must be stratified with respect to recursion and aggregates, and the same holds for most deductive database systems. Therefore, the aggregates in recursion challenge has been the focus of some of the best research work in the deductive database area [8,7,22,20,31,34,23]. Of particular interest, there is the work by Ross and Sagiv [23] who showed that, for each aggregate, a particular lattice can often be found, where this aggregate defines monotone transformations. The difficulty of automatically identifying such lattices [31] User Defined Aggregates for ....

Carlo Zaniolo, N. Arni, and K. Ong. "Negation and Aggregates in Recursive Rules: the LDL++ Approach." DOOD, 1993.

....logicbased semantics of deductive databases. In this section however, we show how N Datalog : can be easily emulated by the Datalog 1S programs with choice, denoted Datalog c 1S . The merits of Datalog 1S for modeling temporal and dynamic systems have, for instance, been described in [12, 45, 7]. In Datalog 1S , predicates may have an additional argument called the stage argument. Values in the stage argument are taken from the domain 0, 0 1, 0 1 1, that is the domain of integers generated by using the infix successor function 1. For instance, the integer 3 is represented as ....

....notation is at the root of the name Datalog 1S . Atoms have the form p(J; t) where J is a stage term and t is a list of terms. Also, in conjunction with recursive Datalog 1S rules, we allow programs to follow a particular form of compilable local stratification, called XY stratification [45]. We now present a technique that given a N Datalog : program produces an XY stratified Datalog c 1S program which is equivalent to N Datalog : i.e. it emulates the non deterministic semantic of such language. The translation is based on a transformation technique introduced in [13] ....

[Article contains additional citation context not shown here]

Zaniolo, C., N. Arni, K. Ong, Negation and Aggregates in Recursive Rules: the LDL++ Approach, in Proc. 3rd Int. Conf. on Deductive and O-O DBs, DOOD-93, Phoenix, AZ, Dec 6-8, 1993, pp. 104--221.

....of these programs that are computationally well behaved were identified and implemented. For instance, current database prototypes support the computation of well founded models for various classes of non stratified programs, which include modularly stratified programs [11, 10] XY stratification [12], and the closely related notion of explicitly locally stratified programs [3, 9] Furthermore, the notion of choice models [7] takes logic based semantics beyond the deterministic realm of well founded models; in fact it identifies a class of programs that always have total stable models of ....

....of this paper is to show that a simple and general solution of the second problem follows naturally from the theoretical and practical advances achieved and implemented on the first front. Therefore, we proceed as follows. In the next section, we recall the concept of XY stratified programs [12], which through their explicit structure of temporal arguments ensure an efficient compilation and computation for their total well founded models. Then, we develop a simple framework to model updates and active rules, using a revised view of intensional versus extensional information. In the ....

[Article contains additional citation context not shown here]

C. Zaniolo, N. Arni, and K. Ong, Negation and aggregates in recursive rules: the LDL++ approach In Procs., International Conference on Deductive and Object-Oriented Databases, DOOD'93, pp. 204-221 1993.

.... exceptions [57, 41] Important classes of programs with nonstratified negation where stable models can be computed in polynomial time include locally stratified programs [35] whose wellfounded models [56, 40] can be derived by an alternating fixpoint procedure [55] and XY stratified programs [59, 22]. Most Datalog languages also support functors, which are used to (i) store complex objects in the database, and (ii) in recursive rules to process structures of unbound length, as to achieve Turing completeness in the language. Extensions of complex objects are supported in deductive ....

C. Zaniolo, N. Arni, and K. Ong. Negation and Aggregates in Recursive Rules: the LDL++ Approach. In Proceedings International Conference on Deductive and Object-Oriented Databases, DOOD'93, 1993.

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C. Zaniolo, N. Arni, K. Ong, "Negation and Aggregates in Recursive Rules: the LDL++ Approach", Proc. 3rd Int. Conf. on Deductive and OODBs, DOOD-93, Phoenix, AZ, December, 1993.

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