R. Krishnamurthy and S. Naqvi. "Non-Deterministic Choice in Datalog. " Proc. 3nd Int. Conf. on Data and Knowledge Bases, pp. 416--424, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(or other set aggregation functions) of a given relation. In this paper, we study the expressive power of languages for both deterministic queries and non deterministic queries. This need has led to the introduction of the choice construct in LDL. The original proposal by Krishnamurthy and Naqvi [19] was later revised by Sacca and Zaniolo [21] and refined in Giannotti, Pedreschi, Sacca and Zaniolo [14] While the declarative semantics of choice models is based on and stable models semantics, it leads to e#cient implementations, and it is actually supported in logic database language [20, ....

....language [20, 8] The objective of this paper is to provide a characterization of the expressive power of various forms of non deterministic constructs. Thus, in addition to FO W(itness) we study the following three languages: Datalog with static choice, i.e. the choice construct in [19], Datalog with lazy dynamic choice, i.e. the choice construct in [21] Datalog with eager dynamic choice, i.e. the choice construct in [14] We show that these languages establish to a hierarchy of increasing expressiveness which we correlate to the non deterministic extensions FO. First, ....

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R. Krishnamurthy, S. Naqvi. Non-Deterministic Choice in Datalog. Proc. 3nd Int. Conf. on Data and Knowledge Bases, Morgan Kaufmann Pub., Los Altos (1988). pp. 416-424.

....an arbitrary choice from the eligible faculty will have to be made and recorded. The desire to express applications as those above, where non deterministic queries and modeling of non deterministic behavior are needed, provided the original motivation for the introduction of the choice construct [KN88]. Only more recently, these authors became fully aware of the important role that these non deterministic constructs can play in computing deterministic queries or transformations. This important facet of the problem is discussed in [AV89] where it is shown that simple deterministic functions ....

....domains [Imm87] The objective of this paper is to revisit the issue of non deterministic extensions to Horn clause based languages from the viewpoints of expressive power and amenability to e#cient implementation. We show that the current proposal, namely the choice proposal described in [KN88] and [NT89] su#ers from undesirable properties that follow from its static nature. Thus, we introduce a new definition called dynamic choice that cures the problems of the construct proposed in [KN88] which will hereafter be referred to as static choice. The declarative semantics of such a ....

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Krishnamurthy, R., and Naqvi, S.A., "Non Deterministic Choice in Datalog ", Proc. 3rd Int. Conf. on Data and Knowledge Bases, Morgan Kaufmann Pub., Los Altos, pp. 416-424, 1988.

....the presence of a suitable stable model, but also that such a model completely characterizes the computation. On the other hand, many alternative stable models of P exist and it is natural to wonder whether all such models can be computed using LD resolution. The simple result below (Theorem 3.2) states that for each fact which is true in an arbitrary stable model, a suitable LD tree exists, which allows one to deduce such a fact. Thus Theorem 3.2 provides a (weak) notion of completeness of LD resolution with respect to the stable model semantics of P . Theorem 1.2. Given a ....

....of P exist and it is natural to wonder whether all such models can be computed using LD resolution. The simple result below (Theorem 3.2) states that for each fact which is true in an arbitrary stable model, a suitable LD tree exists, which allows one to deduce such a fact. Thus Theorem 3.2 provides a (weak) notion of completeness of LD resolution with respect to the stable model semantics of P . Theorem 1.2. Given a program P and a stable model M of P , for each A G M there exists a goal G with respect to P such that A G Mo. Proof. The theorem is easily established by the ....

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R. Krishnamurthy and S.A. Naqvi, "Non-Deterministic Choice in Datalog," Proceedings of the Third International Conference on Data and Knowledge Bases, 1988, pp. 416-424.

....intended semantics: Find an arbitrary student for each course. As this example illustrates, there is a real need for don t care non determinism in logic programming applications. To satisfy this strong need, special constructs were introduced, such as the declarative constructs of choice in LDL [KN,NT], the witness operator in [AV] and the procedural cut construct in Prolog (although the cut serves many other purposes as well) However, no special construct is needed once a stable model semantics is used for logic programs, since the (multiple) stable models semantics subsumes the LDL choice ....

.... the cut serves many other purposes as well) However, no special construct is needed once a stable model semantics is used for logic programs, since the (multiple) stable models semantics subsumes the LDL choice con stmct, which, in turn, provides a declarative substitute to Prolog s cut [KN]. The well founded model semantics is not suitable for the example application, inasmuch as it produces a partial model that blurs the meaning by assigning an undefined classification to all the a st facts listed above. The contribution of this paper is three fold: 1) an in depth study of the ....

[Article contains additional citation context not shown here]

Krishnamurthy, R. and Naqvi, S.A., "NonDeterministic Choice in Datalog", Proc. 3rd Int. Conf. on Data and Knowledge Bases, Morgan Kaufmann Pub., Los Altos, 1988, pp. 416-424.

....In particular, we discuss how it is possible to support ecient history insensitive temporal reasoning by means of real side e ects during the iterated computation [13] Related Work. Nondeterminism is introduced in deductive databases by means of the choice construct. The original proposal in [11] was later revised in [17] and re ned in [8] These studies exposed the close relationship connecting nonmonotonic reasoning with nondeterministic constructs, leading to the de nition of a stable model semantics for choice. While the declarative semantics of choice is based on stable model ....

R. Krishnamurthy and S. Naqvi. Non-deterministic Choice in Datalog. In Proc. 3rd Int. Conf. on Data and Knowledge Bases, pages 416-424, 1988.

....[9, 14] while the material in Sections 4 and 5 is new. In conclusion, this paper provides a thorough account of the pragmatics, semantics and implementation of Datalog . Related Work. Nondeterminism is introduced in deductive databases by means of the choice construct. The original proposal in [17] was later revised in [23] and refined in [12] These studies exposed the close relationship connecting nonmonotonic reasoning with nondeterministic constructs, leading to the definition of a stable model semantics for choice. While the declarative semantics 2 of choice is based on stable model ....

R. Krishnamurthy and S. Naqvi. Non-deterministic Choice in Datalog. In Proc. 3rd Int. Conf. on Data and Knowledge Bases, pages 416--424, 1988.

.... a total order is assumed for the universe, an assumption that would violate the genericity principle [2] Moreover, the version of choice supported in LDL is more powerful than other nondeterministic constructs, such as the witness operator [2] and an earlier version of choice proposed in [23] (called static choice in [18] For instance, the following query cannot be expressed in standard Datalog (since it is nondeterministic) nor it can be expressed by the early version of choice [23] or by the witness construct [2] these early constructs express nondeterminism in nonrecursive ....

.... constructs, such as the witness operator [2] and an earlier version of choice proposed in [23] called static choice in [18] For instance, the following query cannot be expressed in standard Datalog (since it is nondeterministic) nor it can be expressed by the early version of choice [23] or by the witness construct [2] these early constructs express nondeterminism in nonrecursive programs, but su#er from inadequate expressive power in recursive programs [18] Example 3 Rooted spanning tree.We are given an undirected graph where an edge joining two nodes, say x and y, is ....

R. Krishnamurthy and S. Naqvi. "Non-deterministic choice in Datalog," In Proceedings of the 3rd International Conference on Data and Knowledge Bases, 1988.

....the procedural (bottom up) semantics of deductive databases in such a way that a subset of query answer is chosen, on the basis of a functional dependency constraint. Successive studies showed that several improvements were needed. Therefore, the original proposal by Krishnamurthy and Naqvi [26] was later revised by Sacc a and Zaniolo [29] and re ned in Giannotti, Pedreschi, Sacc a and Zaniolo [16] These studies also exposed the close relationship connecting nonmonotonic reasoning with non deterministic constructs, leading to the de nition of a stable model semantics for choice. While ....

....studied, with the aim of: # clarifying the relationships among their procedural, declarative and xpointsemantics, and # comparing their power of expressing deterministic and non deterministic queries. More precisely we will compare: # Datalog with static choice, i.e. the choice construct in [26], both without negation, and with strati ed negation. # Datalog with lazy dynamic choice, i.e. the choice construct in [29] both without negation, and with strati ed negation. 2 # Datalog with eager dynamic choice, i.e. the choice construct in [16] # ## W(itness) and in ationary xpoint ....

[Article contains additional citation context not shown here]

R. Krishnamurthy, S. Naqvi. Non-Deterministic Choice in Datalog. In Proc. 3nd Int. Conf. on Data and Knowledge Bases, Morgan Kaufmann Pub., Los Altos (1988). pp. 416-424.

.... the data independence principle of genericity [5, 1] The expressive power of the choice construct has been studied in [11, 12] where it is shown that it is more powerful than other nondeterministic constructs, including the witness operator [2] and the original version of choice proposed in [15], which is called static choice, to distinguish it from the dynamic choice used here [10] For instance, it has been shown in [10] that the task of ordering a domain or computing whether a relation contains an even number of elements (parity query) cannot be performed by positive programs with ....

Krishnamurthy R. and S. Naqvi. Non-deterministic choice in Datalog. In Proc. of the 3rd International Conf. on Data and Knowledge Bases, 1988.

....because different outcomes depending of the order used will be possible. Two main non deterministic constructions have been proposed in query languages: the witness operator of [1] which, applied on a relation R, allows to choose non deterministically a tuple of R and the choice construct of [11,13,14] in Datalog programs which allows to introduce particular goals (the so called choice goals) in the premises of the rules. Such choice goals are of the form Choice( X) Y) where X and Y are lists of variables and their function is to enforce the functional dependency X Y to the intensional ....

....to the stable semantics i.e. each so computed set of facts is a stable model of P and conversely each stable model of P can be computed by the SBF procedure. 3. Non deterministic choice constructs 3.1. Model theoretical semantics for choice construct The choice construct, firstly introduced in [11,13,14] , is used to enforce functional constraints on the facts derived from a logic program. Following [14] negation less choice programs are positive Datalog programs in which special goals called choice goals are allowed: a choice goal is an atom of the form Choice( X) Y) where X and Y are lists ....

Krisnamurthy R., Naqvi S. . Non-Deterministic Choice in Datalog. Proc. 3nd Int. Conf. on Data and Knowledge Bases, Morgan Kaufman Pub., Los Altos (1988) p. 416-424.

.... of genericity (Abiteboul et al. 1995) The expressive power of choice was studied in (Giannotti et al. 2000) where it was shown that it is more powerful than other nondeterministic constructs, such as the witness operator (Abiteboul et al. 1995) and the original version of choice proposed in ( Krishnamurthy and Naqvi, 1988); e.g. these other Nonmonotonic Reasoning in LDL 531 operators can neither order domains nor express the parity query (Giannotti et al. 1991) Example 4 Rooted spanning tree. We are given an undirected graph where an edge joining two nodes, say x and y, is represented by the pair g(x; y) ....

Krishnamurthy, R., Naqvi, S. (1988) Non-Deterministic Choice in Datalog. Proc. 3nd Int. Conf. on Data and Knowledge Bases, pp. 416-424, Morgan Kaufmann, Los Altos (1988).

....with so called least unde ned partial stable (L stable) models [46] for normal logic programs (DATALOG : L stable ) which are a relaxation of the concept of stable model. An alternative to allow negation in DATALOG in order to increase expressive power is the choice operator introduced in [47]. Roughly, the choice operator allows for atoms choice(x; y) in rule bodies, which choose precisely one instantiation of the y variables for each instantiation of the x variables. Since several possibilities exist for that in general, the language computes non deterministic queries (i.e. several ....

R. Krishnamurthy and S.A. Naqvi, \Nondeterministic Choice in Datalog", in Proceedings 5th Intl. Conf. on Data and Knowledge Bases, Los Altos, 1988, pp. 416-424, Morgan Kaufmann Publishers, Inc.

....In particular, we discuss how it is possible to support efficient history insensitive temporal reasoning by means of real side effects during the iterated computation [13] Related Work. Nondeterminism is introduced in deductive databases by means of the choice construct. The original proposal in [11] was later revised in [17] and refined in [8] These studies exposed the close relationship connecting nonmonotonic reasoning with nondeterministic constructs, leading to the definition of a stable model semantics for choice. While the declarative semantics of choice is based on stable model ....

R. Krishnamurthy and S. Naqvi. Non-deterministic Choice in Datalog. In Proc. 3rd Int. Conf. on Data and Knowledge Bases, pages 416--424, 1988.

....In fact for a query goal g(X) we might have multiple stable models all sharing the same values of the g predicates. 3 Non determinism and Functional Dependencies Early attempts at introducing non determinisms rule based languages are the Witness operator [2] and the Static Choice operator [30]. Although these two were defined quite independently they share profound similarities, beginning with the usage of the notion of Functional Dependencies (FDs) for their definitions. Witness Operator An important non deterministic extension of FO uses the witness operator [2, 3] Let J be a ....

....construct for declaring and enforcing FDs in Datalog. Observe that Datalog :s , i.e. Datalog with stratified negation, cannot express a non deterministic query; e.g. it cannot select an arbitrary advisor for a student out of a set of several eligible advisors. The original definition of choice [30, 32] relies on the re writing of the program into one where the original choice rule is broken in three parts. For instance, the program of Example 2 is basically rewritten as follows (using a mixed algebra rules notation where chosen and extchoice denote the binary relations corresponding to the ....

[Article contains additional citation context not shown here]

R. Krishnamurthy and S. Naqvi, Non-deterministic choice in Datalog, in Proceedings of the 3rd International Conference on Data and Knowledge Bases, 1988, pp. 416--424.

....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 the meaning of this program. For instance the following program, assign to each student an advisor from the ....

.... relation between students and professors (sharing the same area) the st ad relation is restricted to be many to one, as a result of the presence of choice(St, Ad) In LDL, this very powerful construct was disallowed in recursion, inasmuch as the functional dependency based semantics proposed in [8] suffers from technical problems such as a lack of justifiability property and its unsuitability to efficient implementation due to its static nature [15] These problems were avoided by using instead a semantics based on the use of negation and stable models [6] For instance, the meaning of the ....

R. Krishnamurthy and S. Naqvi. "Non-deterministic choice in Datalog," In Proceedings of the 3rd International Conference on Data and Knowledge Bases, 1988.

....by the LDL system [2] Our approach builds on the choice construct, where formal logic based semantics, usability in programming and computational efficiency have successfully converged a second example of such a convergence after stratification. The idea of choice was introduced in [11] 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 models defining the meaning of this program, whereby the following program assigns to each student an advisor from the same ....

.... between students and professors (sharing the same area) the st ad relation is restricted to be many to one, as a result of the presence of choice( St) Ad) In LDL, this very powerful construct was disallowed in recursion, inasmuch as the functional dependency based semantics proposed in [11] suffers from technical problems such as a lack of justifiability property and its unsuitability to efficient implementation due to its static nature [21] These problems were solved by using, instead, a semantics based on the use of negation and stable models [8] For instance, the meaning of the ....

R. Krishnamurthy and S. Naqvi. "Non-deterministic choice in Datalog," In Proceedings 3rd Int.Conference on Data and Knowledge Bases, 1988.

.... that could not be expressed otherwise [10, 8] In fact, the expressive power of the choice construct has been studied in [9, 10] where it is shown that it is more powerful than other nondeterministic constructs, including the witness operator [2] and the original version of choice proposed in [13], which is called static choice, to distinguish from the dynamic choice used here [8] For instance, it has been shown in [8] that the task of ordering a domain or computing whether it contains an even number of elements (parity query) cannot performed by positive programs with static choice or ....

Krishnamurthy R. and S. Naqvi. Non-deterministic choice in Datalog. In Proc. of the 3rd International Conf. on Data and Knowledge Bases, 1988.

....means that there is no reason to consider non stratified aggregation due to lack of expressive power. Several issues need to be explored further. One is the incorporation of function symbols into the input and output domains. Another interesting question is how should nondeterministic queries [10, 6] be defined and computed. Certain types of non determinism can be introduced into D af by allowing different encodings to lead to different answers. Each permutation of domain elements thus represents a possible choice. Acknowledgements We thank the anonymous referees for comments that ....

R. Krishnamurthy and S. A. Naqvi. Non-deterministic choice in datalog. In Proceedings of the 3rd International Conference on Data and Knowledge Bases, pages 416--424, 1988.

....update like [q : X)OE] the base relation q can play the role of a cursor. Using the methods introduced in Section 3.6, one can iterate over the relation q one tuple at a time, just like an SQL cursor. T R can thus be seen as a formal basis for embedded SQL. 3. 4 Non Deterministic Sampling In [24], Krishnamurthy and Naqvi proposed the so called choice operator. They argued that non deterministic choice is needed to write queries such as, Produce a sample of one employee from each department. The idea was to introduce a special construct, choice( X) Y ) that selects those ....

....d) p(a; d)gi [p 1 2 : q] In practice, this transition base would probably be enumerated by a special procedure written in a language like C. The important point here is that the semantics of T R allows such procedures. Thus we do not have to explicitly construct a choice operator, unlike in [24, 30]. Instead, it falls out naturally from the semantics of T R as a special case. 3.5 Hypothetical Reasoning Hypothetical queries play an important role in reasoning about knowledge [9] Because of such queries, it is often necessary to perform hypothetical updates as well as actual ones. For ....

R. Krishnamurthy and S. Naqvi. Non-deterministic choice in Datalog. In Proceedings of the 3-d Intl. Conference on Data and Knowledge Bases, pages 416--424. Morgan-Kaufmann Publ., 1988.

....is it possible to introduce fixed and variable predicates in the definition of WST and WSU in the style of the ECWA 3. In [29] Sacc a and Zaniolo show how the stable model semantics can be used to declaratively specify the behavior of the choice operator introduced by Krishnamurthy and Naqvi in [17]. We are currently investigating the feasibility of using weakly stable models to specify generalized choice operators. 4. Examine for which class of disjunctive databases WST and WSU are polynomially tractable. One direction that may be promising is using Ben Eliyhau and Dechter s [2] idea of ....

R. Krishnamurthy and S. A. Naqvi. Non-deterministic choice in datalog. In Proceedings of the Third International Conference on Data and Knowledge Bases, pages 416--424. Morgan Kaufmann, Los Altos, 1988.

....the following are equivalent: ffl is in ndb ptime, ffl is defined by a N Datalog : program, and ffl is defined by a N Datalog : 8 program. 6. 3 The choice operator Another way to provide nondeterminism in rule based languages is provided by the choice operator first presented in [KN88] This construct has been included in the language LDL, an implementation of Datalog : NT89] Variations of the choice operator, and its connection with stable models of Datalog : programs, are further studied in [SZ90, GPSZ91] The expressive power of the choice operator in the context of ....

R. Krishnamurthy and S.A. Naqvi. Nondeterministic choice in datalog. In 5th Int'l. Conf. on Data and Knowledge Bases, pages 416--424, Los Altos, CA, 1988. Morgan Kaufmann.

....an update like [q : X)OE] the base relation q can play the role of a cursor. As we shall see in Section 3.6, T R can iterate over this cursor one tuple at a time, just as in embedded SQL. T R , thus, can seen as a formal basis for cursors in embedded SQL. 3. 4 Non Deterministic Sampling In [23], Krishnamurthy and Naqvi proposed the so called choice operator. They argued that nondeterministic choice is needed to write queries such as, Produce a sample of one employee from each department. The idea was to introduce a special construct, choice( X) Y ) that selects those ....

.... d) p(a; b)gi [p 1 2 : q] hfq(a; b) q(a; c) q(a; d)g; fq(a; b) q(a; c) q(a; d) p(a; c)gi [p 1 2 : q] hfq(a; b) q(a; c) q(a; d)g; fq(a; b) q(a; c) q(a; d) p(a; d)gi [p 1 2 : q] The important point here is that we do not have to explicitly construct a choice operator, unlike in [23, 29]. Instead, it falls out naturally from the semantics of T R. 3.5 Hypothetical Reasoning Hypothetical queries play an important role in reasoning about knowledge [9] Because of such queries, it is often necessary to perform hypothetical updates as well as actual ones. For instance, a gameplaying ....

R. Krishnamurthy and S. Naqvi. Non-deterministic choice in datalog. In Proceedings of the 3-d Intl. Conference on Data and Knowledge Bases, pages 416--424. Morgan-Kaufmann Publ., 1988.

....di#cult problem of formalizing their semantics was solved through the use of dynamic logic [Har] The semantics so defined reduces to first order logic in the absence of updates. Finally, the notion of functional dependencies was used to support nondeterminism through a construct called choice [KrN1]. 2.2 The Compilation Problem The LDL compiler performs several functions, beginning with the parsing of the rules into a Predicate Connection Graph (PCG) KeOT] and ending with the code generation phase. Some details of this complex process are discussed in Section 3, others are beyond the ....

Krishnamurthy and S. Naqvi, "Non-Deterministic Choice in Datalog, " Proc. 3rd Int. Conf. on Data and Knowledge Bases, June 27--30, Jerusalem, Israel.

....difficult problem of formalizing their semantics was solved through the use of dynamic logic [Har] The semantics so defined reduces to first order logic in the absence of updates. Finally, the notion of functional dependencies was used to support nondeterminism through a construct called choice [KrN1]. 2.2 The Compilation Problem The LDL compiler performs several functions, beginning with the parsing of the rules into a Predicate Connection Graph (PCG) KeOT] and ending with the code generation phase. Some details of this complex process are discussed in Section 3, others are beyond the ....

Krishnamurthy and S. Naqvi, "Non-Deterministic Choice in Datalog, " Proc. 3rd Int. Conf. on Data and Knowledge Bases, June 27--30, Jerusalem, Israel.

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R. Krishnamurthy and S. Naqvi. "Non-Deterministic Choice in Datalog. " Proc. 3nd Int. Conf. on Data and Knowledge Bases, pp. 416--424, 1988.

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