D. B. Kemp and P. J. Stuckey. Semantics of Logic Programs with Aggregates. In ILPS, pages 387--401. MIT Press, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....meaning to Example 2, by rewriting it using negation, as in the previous example, we obtain a non stratified program, with all the accompanying semantics and computational problems: the answer (under the well founded semantics) could contain undefined atoms and the computation could be ine#cient. [6,7,10,12,13,17,22,28,29,32,34,38]. In this paper we consider the problem of taking a program such as that of Example 1, where a min predicate is given as a post condition on a recursive graph computation, and transform the program into an equivalent one where the min predicate is pushed into the recursive rules. Once a query is ....

Kemp, D., and Stuckey, P., Semantics of Logic Programs with Aggregates. Proc. of the 1991 Intern. Symposium on Logic Programming, 387--341 (1991).

....[10] Indeed, this very useful extension requires that partial results and early returns be produced during the computation, rather than at the end of the computation as in SQL3 TERMINATE. A substantial amount of previous work has focused on aggregates and their semantics in logic based programs [3, 2, 14, 13, 15, 19]. Of particular significance is the work on monotonic aggregation [15] since monotonic aggregates can be used to express very useful 1 recursive queries (e.g. for Bill of Materials and least distance paths in a graph) that have posed a long standing challenge to relational DB languages. As ....

....by the inflationary repeated application of such a nondeterministic mapping. Furthermore the set of these fixpoints coincide with the stable models [6] of the program obtained by rewriting the choice program into an equivalent program with negation [16] Therefore, keeping with previous authors [13], we have defined the semantics of aggregates in terms of stable models [6] however, through the use of the choice construct, we have avoided the computational intractability problems of stable models. Indeed in our formal semantics of aggregates, choice rules are only used to deliver the next ....

David B. Kemp and Peter J. Stuckey. "Semantics of logic programs with aggregates" Proc.

....extended successfully with a limited form of aggregate constraints [16] 22] describes an extension of an abductive system with aggregates and some experiments with this system in the context of scheduling and puzzles. As will be shown in section 5, current extensions of well founded semantics [12, 18, 19] and stable model semantics [12, 16] of programs with aggregates are still weak in some ways. In this paper, we propose a stronger extension of the well founded and stable model semantics for logic programs with aggregates. Our approach uses Approximation Theory developed in [5] With each ....

....of aggregate constraints [16] 22] describes an extension of an abductive system with aggregates and some experiments with this system in the context of scheduling and puzzles. As will be shown in section 5, current extensions of well founded semantics [12, 18, 19] and stable model semantics [12, 16] of programs with aggregates are still weak in some ways. In this paper, we propose a stronger extension of the well founded and stable model semantics for logic programs with aggregates. Our approach uses Approximation Theory developed in [5] With each nonmonotone operator, this theory ....

[Article contains additional citation context not shown here]

D. B. Kemp and P. J. Stuckey. Semantics of logic programs with aggregates. In V. A. Saraswat and K. Ueda, editors, Proceedings of the International Logic Programming Symposium, pages 387-401. MIT Press, 1991.

....to give a meaning to Example 2 by its rewriting using negation, as in the previous example, we obtain a non strati ed program, with all the open semantic and computational issues therewith. These problems, widely recognized by deductive database researchers, have been the subject of recent works [4, 13, 7, 20, 10, 17]. These works however, consider the general problem of aggregates, e.g. including average, sum, etc. Our paper focuses only on extrema aggregates and proposes specialized, and thus very ecient, techniques for handling them. Although our discussion deals explicitly only with min programs, the ....

D. Kemp and P. Stuckey. Semantics of Logic Programs with Aggregates. In Proceedings of the 1991 Intern. Symposium on Logic Programming, pages 387-341, 1991.

....added to the same language. More recently, Mumick et al. MPR90] Ganguly et al. GGZ91, GZG92] Lefebvre [Lef91] and Sudarshan and Ramakrishnan [SR91] discuss extensions of Datalog with aggregates and the associated optimization problem. Similarly, Beeri et al. BRSS92] Kemp and Stuckey [KS91], Ross and Sagiv [RS92] and Van Gelder [VG92] propose alternate semantics for aggregates in logic programs and deductive databases. Some authors have considered aggregation on top of general set manipulation in the context of logic languages or complex object models [AB88, TZ86] However, we are ....

....aggregation. The simplicity of the condition is due to the fact that aggregation occurs in the heads of rules, instead of in the bodies (as it is the case in [MPR90] 2 We omit presenting the model based version of the semantics of stratified Datalog programs with non recursive aggregation (see [MPR90, KS91, RS92, VG92]) since our results are based on the equivalent operational semantics given by Algorithm 2.1. 6 Algorithm 2.1: Evaluation of stratified Datalog with non recursive aggregation. input: A stratified Datalog program with aggregation P p and a finite database d = r 1 ; r m ) over D and N ....

David Kemp and Peter Stuckey. Semantics of logic programs with aggregates. In Proceedings of the International Logic Programming Symposium, pages 387--401, 1991.

....in database querying. An aggregate operation is a function that maps a set to some value, e.g. the maximum or minimum in the set, the cardinality of this set, the summation of all its members, etc. This has been a topic of considerable interest in the deductive database literature recently [8, 17, 21, 31, 32, 34]. In considering the problems with various semantic approaches, Van Gelder notes that, for many applications in which the use of aggregates has been proposed, the concept of subset is what is really necessary [34] Moreover, for many problems requiring aggregate operations to be performed, the ....

D.B. Kemp and P.J. Stuckey, Semantics of Logic Programs with Aggregates, Proc. Intl. Logic Programming Symposium, pp. 387--401, MIT Press, 1991.

....y This paper is TR 93 040, Department of Computer Science, SUNY Buffalo, November 1993. Comments are welcome, and may be sent to any of the authors. 0 1. Introduction In recent years there has been considerable interest in the topic of aggregation in logic programming and deductive databases [MPR90, KS91, RS92, V92, GSZ93, SSRB93]. An aggregate operation is a function that maps a set to some value, e.g. the maximum or minimum in the set, the cardinality of this set, the summation of all its members, etc. In considering the problems with various semantic approaches, Van Gelder [V92] notes that, for many problems in which ....

D.B. Kemp and P.J. Stuckey, "Semantics of Logic Programs with Aggregates," Proc. ILPS 91, pp. 387-401, San Diego, 1991. 14

....and can be arbitrary sets of constraints. Considering the rule p(X; Y ) 0 X;X Y: X = Y is a correct answer to the query min(p(X; Y ) Y Gamma X) The definition of OCLP programs does not exclude recursion though optimization predicates. A similar problem is discussed in [1] and [2] where the stratified semantics of aggregates are generalized using the well founded and stable model semantics of logic programs. In the context of OCLP programs, the natural theory to apply is Fitting Kunen s 3 valued semantics, which does not coincide with stratified and wellfounded semantics. ....

D.B. Kemp, P.J. Stuckey, "Semantics of logic programs with aggregates", Proc. of ILPS'91, San Diego, pp.387-401. 1991.

....quite efficiently, as we have shown in our recent work [21] We show that partial order clauses help render clear and concise formulations to problems involving aggregate operations and recursion in database querying. This has been a topic of considerable interest in the literature recently [15, 26, 27, 29]. An aggregate operation is a function that maps a set to some value, e.g. the maximum or minimum in the set, the cardinality of this set, the summation of all its members, etc. In considering the problems with various semantic approaches, Van Gelder [29] notes that, for many problems in which ....

D.B. Kemp and P.J. Stuckey, Semantics of Logic Programs with Aggregates, Proc. Intl. Symp. on Logic Programming, pp. 387-401, MIT Press, 1991.

....in conjunction with negation. Both the semantics apply only to restricted classes of programs, and in the case of Ross and Sagiv, it is undecidable whether a program falls into their class (i.e. is monotonic) or not. Our semantics applies to all programs. The semantics of Kemp and Stuckey [KS91] also applies to all programs, but leaves all of accept(a) accept(b) and accept(c) undefined. The semantics of Van Gelder applies to all programs, as well, but it too makes all of accept(a) accept(b) and accept(c) undefined, which Van Gelder says (and we agree) is undesirable. Van Gelder ....

....focusing on the cheapest path program, we have tried to point out that many programs in this class can be evaluated efficiently, indeed more efficiently than equivalent programs (at least, some natural alternatives) outside this class. 7 Relation to Other Semantics Kemp and Stuckey s semantics [KS91] and the original valid semantics [BRSS92a] insisted that a set be fully defined before aggregation could be performed on it. This leaves too many values undefined, since information about partially constructed sets cannot be used. Van Gelder [Van92] and Ross and Sagiv [RS92] allowed derivations ....

[Article contains additional citation context not shown here]

David Kemp and Peter Stuckey. Semantics of logic programs with aggregates. In Proceedings of the International Logic Programming Symposium, pages 387--401, San Diego, CA, U.S.A., October 1991.

.... [109] 39] 9] 22] 51] 133] 99] 135] 101] 52] 42] 43] 54] 93] 107] 108] 31] XSB, YAP, Lola, and others Optimizations [36] 5 Overview ffl Magic Sets and Related Research (e.g. Alexander Method) Formulation [102] 7] 111] 124] 20] 87] 85] 10] [70], 91] 117] 47] 60] 96] 11] 114] 104] 84] References are a little dated. Implementation and Systems [8] 25] 125] 97] 113] 130] 131] 44] 59] 63] 86] LDL, Aditi, Coral and others. Optimizations [95] 88] 105] 106] 103] 72] 116] 62] 61] ....

D. Kemp and P. Stuckey. Semantics of logic programs with aggregates. In ILPS, pages 387--404, 1991.

.... 8 c; l; r; rc; n: room of lecture(l; r) capacity(r; rc) course(l; c) Card(fstjenrolled(st; c)g; n) rc n Other frequently occurring aggregates are summation, minimum, maximum, etc : Therefore aggregates are extensively studied in logic programming and deductive databases [16, 20, 17]. A natural choice of the alphabet al..so poses requirements on the level of problem solving capabilities of the used logic. Illustrated in the domain of university lecture scheduling, some basic concepts are lectures, time slots, rooms. Basic relations between these concepts describe when and ....

....of the completion of the de nition [2] Below, completed de nitions of predicates will be denoted: 8(p(X) B p [X] We call from now on B p [X] the completion of p. 2.2 Aggregates As mentioned in the introduction, aggregates have been studied in logic programming and deductive databases. [16, 20, 17] proposed extensions of logic programming with aggregates and showed how aggregate expressions can be transformed and reduced to recursive logic programs using certain schemata. These transformations de ne at the same time the declarative and procedural semantics for these extensions. This work ....

David B. Kemp and Peter J. Stuckey. Semantics of logic programs with aggregates. In Kazunori Saraswat, Vijay; Ueda, editor, Proceedings of the 1991 International Symposium on Logic Programming (ISLP'91), pages 387-404, San Diego, CA, October 1991. MIT Press.

....by the inflationary repeated application of such a nondeterministic mapping. Furthermore the set of these fixpoints coincide with the stable models [9] of the program obtained by rewriting the choice program into an equivalent program with negation [20] Therefore, keeping with previous authors [16], we have defined the semantics of aggregates in terms of stable models [9] however, through the use of the choice construct, we have avoided the computational intractability problems of stable models. Indeed in our formal semantics of aggregates, choice rules are only used to deliver the next ....

David B. Kemp and Peter J. Stuckey, "Semantics of logic programs with aggregates" Proc. 1991 International Symposium on Logic Programming, pages 387--401, October 1991.

....in order to make the language more expressive. In [33] Chandra and Harel represent arithmetic operators as infinite relations over the set of numbers. The standard declarative semantics, bottom up and top down query evaluation procedures have been extended to incorporate aggregate operators [60, 75, 85, 92, 94, 104]. Example 2.1.3 Consider a database that stores information about employees in the form employee(Name; Dept; Salary) Using aggregates, it is possible to define a clause to determine the average salary for each department. avg salary per dept(Dept; AvgSal) group by(employee(Name; Dept; ....

D. B. Kemp and P. J. Stuckey. Semantics of logic programs with aggregates. In V. Saraswat and K. Ueda, editors, Proc. 1991 International Logic Programming Symposium, pages 387--401, San Diego, USA, 1991.

....problems, and to incorporate new logic programming paradigms such as constrained logic programming and concurrent logic programming in the nonmonotonic framework. Extensions of the languages by allowing more complex data such as sets and aggregates are very important in database applications [KS91, BRSS92, Gel92a]. Even more questions remain for noncategorical programs, i.e. logic programs with multiple answer sets or disjunctive logic programs. In this case one of the most important problems seems to be the lack of clear procedural interpretation of rules of a program. Such interpretation of definite ....

D. Kemp and P. Stuckey. Semantics of logic programs with aggregates. In Proceedings of International Symposium on Logic Programming, pages 387--401, 1991.

.... 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 and Related Research (e.g. Alexander Method) Formulation [87] 5] 97] 111] 18] 69] 67] 8] [59], 73] 103] 39] 49] 79] 9] 101] 89] 66] Implementation and Systems [6] 24] 112] 80] 99] 118] 119] 37] 48] 52] 68] Optimizations [78] 70] 90] 91] 88] 61] 102] 51] 50] 104] 16] ffl Bibliography is incomplete: it considers only ....

D. Kemp and P. Stuckey. Semantics of logic programs with aggregates. In International Logic Programming Symposium, pages 387--404, 1991.

....the bottom up evaluation of such programs. In presence of function symbols the undertaken canonical model approach to the declarative semantics of deductive databases is not viable however as such semantics then become highly undecidable, and can be used only for restricted classes of CLP programs [16]. In the general context of constraint logic programming we have to rely on the weaker standard three valued logical semantics of the program s completion [14] This means that when skipping from deductive databases to general constraint logic programming we have to trade the implicit expressive ....

D.B. Kemp, P.J. Stuckey, "Semantics of logic programs with aggregates", International Logic Programming Symposium, ILPS'91, Paris, pp.387-401, MIT Press, 1991.

....1. specification of the constraints of the problem; 2. specification of what is to be optimized; and 3. specification of the criteria for determining the optimal solution. While several approaches to optimization have been proposed in the logic programming and deductive databases literature [20, 23, 32, 43, 48, 61, 67, 77, 84], they do not allow one to fully specify all three of the above components. Our thesis is that the concept of preference provides a natural, modular, declarative, and efficient way for expressing the three components of an optimization problem. We describe a principled extension of constraint ....

....such as maximize and minimize, although the semantics of such meta level operators is usually not provided. Furthermore, the criteria for ordering the solutions have no explicit status in the model theory as the semantics of optimization (when it is discussed) is usually provided through negation [20, 23, 48, 65]. 2.1.3 Logic of Preference The syntax of the logic of preference introduced by Mantha [63] extends the syntax of first order logic by introducing a modal operator P f with the rule of formation: if F is a formula then so is P f F . Following the model tradition in modal logic enunciated by ....

[Article contains additional citation context not shown here]

D. B. Kemp and P. J. Stuckey. Semantics of Logic Programs with Aggregates. In Proc. International Logic Programming Symposium, 1991.

....of extreme value aggregate operations (such as min and max) in deductive databases. A program with such aggregate operations has an equivalent first order formulation using negation. There has been a considerable interest recent years in providing a satisfactory semantics for aggregate operations [3, 11, 17, 21, 24]. Ganguly et al. [3] considered first order aggregates and showed that under certain monotonicity conditions, the firstorder equivalent program has a total well founded model [25] that can be computed using a greedy fixed point procedure. Kemp and Stuckey [11] examined programs with recursion ....

....for aggregate operations [3, 11, 17, 21, 24] Ganguly et al. [3] considered first order aggregates and showed that under certain monotonicity conditions, the firstorder equivalent program has a total well founded model [25] that can be computed using a greedy fixed point procedure. Kemp and Stuckey [11] examined programs with recursion through aggregation. To give semantics for programs with aggregation, they extended two well known semantics for programs with negation, namely, well founded models and stable models [4] Ross and Sagiv [17] provide semantics for aggregation here the domain over ....

D. B. Kemp and P. J. Stuckey. Semantics of Logic Programs with Aggregates. In Proc. International Logic Programming Symposium, 1991.

....of all those alphabetic order challenged, led a successful crusade to have the names in reverse alphabetical order. three valued stable model semantics [9] provided semantics for programs with general (non stratified) negation. Semantics that allow non stratified aggregation were proposed in [2, 5], but they leave too many facts undefined. Recently, there have been several proposals to define semantics that take into account special properties of aggregate operations [4, 13, 14] Most of the above semantics are three valued, i.e. in models based on these semantics, facts may be true, false ....

....aggregate valid semantics as well as the aggregate well founded semantics, which we present in this paper. The semantics of Mumick et al. [7] and Ross and Sagiv [13] are not applicable on the above program since it uses aggregation in conjunction with negation. The semantics of Kemp and Stuckey [5] leaves all of accept(a) accept (b) and accept(c) undefined, as does the semantics of Van Gelder [14] which Van Gelder says (and we agree) is undesirable. We note that none of the above semantics, except for [13] treats programs as a set of equations to be solved. Doing so in the above example ....

[Article contains additional citation context not shown here]

D. Kemp and P. Stuckey. Semantics of logic programs with aggregates. In Procs. of the International Logic Programming Symposium, pages 387--401, San Diego, CA, U.S.A., Oct. 1991.

....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 ....

David B. Kemp and Peter J. Stuckey. "Semantics of logic programs with aggregates" Proceedings of the 1991 International Symposium on Logic Programming, pages 387--401, October 1991.

....problems, and to incorporate new logic programming paradigms such as constrained logic programming and concurrent logic programming in the nonmonotonic framework. Extensions of the languages by allowing more complex data such as sets and aggregates are very important in database applications [KS91, BRSS92, Gel92a]. Even more questions remain for noncategorical programs, i.e. logic programs with multiple answer sets or disjunctive logic programs. In this case one of the most important problems seems to be the lack of clear procedural interpretation of rules of a program. Such interpretation of definite ....

D. Kemp and P. Stuckey. Semantics of logic programs with aggregates. In Proceedings of International Symposium on Logic Programming, pages 387--401, 1991.

No context found.

D. B. Kemp and P. J. Stuckey. Semantics of Logic Programs with Aggregates. In ILPS, pages 387--401. MIT Press, 1991.

No context found.

D. B. Kemp and P. J. Stuckey. Semantics of logic programs with aggregates. In Proc. of the Int. Logic Programming Symposium, pages 387--401. MIT Press, 1991.

No context found.

David B. Kemp and Peter J. Stuckey. Semantics of Logic Programs with Aggregates. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 387--401. MIT, June 1991.

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