Catriel Beeri, Raghu Ramakrishnan, Divesh Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Proceedings of the Eleventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 91--104, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of different aggregate operators 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 ....

Catriel Beeri, Raghu Ramakrishnan, Divesh Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Proceedings of the Eleventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 91--104, 1992.

....based on that model, the program is rewritten to make clauses definite. Using these definite clauses, a fixpoint is reached with a new model. The process of finding a model, and rewriting program clauses to make them definite continues until a larger fixpoint is reached. In approaches like [79] or [6], this iterated fixpoint is central to the formulation of the evaluation method, while in SLG it is perhaps less obvious. In SLGO , a system of clauses may be evaluated until only suspended and answer clauses remain. At completion, the suspended clauses are either reactivated, or delayed. In a ....

C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In 11th PODS, pages 91 -- 103, 1992.

....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 ....

C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Proceedings of Principles of Database Systems, pages 91--104, 1992.

....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 ....

C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Proceedings of Principles of Database Systems, pages 91--104, 1992.

....model semantics [Prz90] and the valid semantics [BRSS92a] define semantics for all logic programs with negation and set grouping. Recently, there have been several proposals to extend the semantics to take into account special properties of aggregate operations [GGZ91, RS92, Van92] Beeri et al. [BRSS92b] note that the valid semantics can be extended to take into account special properties of some aggregate operations such as min and max. We present a motivating example in Section 1.1, that illustrates the drawbacks of current semantics for nonstratified aggregation. In this paper, we consider ....

....the Herbrand universe of the program along with the database is used. Unless otherwise specified, the domain of a set and a three valued set is the universe. 1 We do not consider non ground facts in this paper, but our results can be generalized to handle non ground facts in a manner similar to [BRSS92b]. 5 3.1 Aggregate Functions Traditionally, aggregate functions have been applied to two valued multisets. We extend aggregate functions to work on three valued multisets for the following intuitive reason. In the course of a computation for a program, facts start off with their truth status ....

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C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Proceedings of the ACM Symposium on Principles of Database Systems, 1992. Manuscript, submitted for publication.

....facts in some intended model. Early approaches restricted the class of programs to those that are stratified in some fashion [ABW88, Prz88, Ros90, PP88] More recent approaches, such as the well founded semantics [VRS91] the three valued stable model semantics [Prz90] and the valid semantics [BRSS92a] define semantics for all logic programs with negation and set grouping. Recently, there have been several proposals to extend the semantics to take into account special properties of aggregate operations [GGZ91, RS92, Van92] Beeri et al. BRSS92b] note that the valid semantics can be extended to ....

....the approach in this paper is based on a normal form computation, and is split into two main parts. The first part defines when a fact follows from a rule and a three valued interpretation (Section 3. 3) The definition of follows from presented in the paper generalizes that presented in [BRSS92a]. The second part defines when a fact can be assumed false based on default rules, and when a derivation is considered aggregate valid. An aggregate valid computation is one where every derivation is aggregate valid. A complete aggregate valid computation (i.e. one that cannot be extended to ....

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C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 91--104, June 1992.

....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 ....

....literal may not be negated. As a special case of restriction G1, a grouping atom can never be a fact. 3.3 Satisfaction We now define when a literal is satisfied in a given interpretation, and when a fact follows from a rule. The definition for rules without aggregation is the same as in [2], although we couch it in a different notation. Definition 3.2 (Satisfaction) Suppose we are given I = hT I ; F I i and a substitution oe. Given a positive non grouping literal q i (t i ) we say that q i (t i ) oe] is satisfied in I if q i (t i ) oe] is covered by T I . Similarly, for a ....

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C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Procs. of the ACM Symp. on Principles of Database Systems, pages 91--104, June 1992.

....functions to be incrementally computed. We also provide upper and lower bounds for incremental computation of a variety of common aggregate functions. Our second contribution is a novel reformulation of the monotonic semantics in terms of computations, following the approach of Beeri et al. [3] (Section 3) The least fixpoint characterization in [14] is very sensitive to the order in which facts are derived. Consequently, using this formulation, it is very difficult to show the correctness of program optimizations, such as the Magic Sets transformation, that change the order in which ....

....optimizations using either the least model or the least fixpoint characterizations of the monotonic semantics can hence be quite difficult. We address the problem by presenting a new formulation of the monotonic semantics in terms of computations , following the proof theoretic approach of [3, 15]. It is much easier to reason about correctness of optimizations using this formulation. 3.1.1 A Proof Theoretic Approach to Semantics The idea behind the proof theoretic approach to semantics [3, 15] is to first define rules for inferring positive information (i.e. which facts are true) and ....

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C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. A proof theoretic approach to semantics for logic programs. Submitted for publication. Parts of the paper appeared in `The Valid Model Semantics for Logic Programs ' (PODS'92), and in `Extending the Well-Founded and Valid Semantics for Aggregation' (ILPS'93)., 1994.

.... of the program [BNR 87] as was discussed for negation) Later approaches allowed weaker forms of stratification such as group stratification and magical stratification [MPR90] or modular stratification [Ros90] or extended the well founded and stable models to deal with aggregates [KS91, BRSS92] In general, if a rule contains grouping in the head, the multiset created by grouping must be fully determined before generating a fact using this rule. For example, if a rule contains p(X; Y ) in the head, for a given X value, the complete multiset of associated Y values must be known in ....

C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. The valid model semantics for logic programs. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 91--104, June 1992.

....functions to be incrementally computed. We also provide upper and lower bounds for incremental computation of a variety of common aggregate functions. Our second contribution is a novel reformulation of the monotonic semantics in terms of computations, following the approach of Beeri et al. [3] (Section 3) The least fixpoint characterization in [14] is very sensitive to the order in which facts are derived. Consequently, using this formulation, it is very difficult to show the correctness of program optimizations, such as the Magic Sets transformation, that change the order in which ....

....optimizations using either the least model or the least fixpoint characterizations of the monotonic semantics can hence be quite difficult. We address the problem by presenting a new formulation of the monotonic semantics in terms of computations , following the proof theoretic approach of [3, 15]. It is much easier to reason about correctness of optimizations using this formulation. 3.1.1 A Proof Theoretic Approach to Semantics The idea behind the proof theoretic approach to semantics [3, 15] is to first define rules for inferring positive information (i.e. which facts are true) and ....

[Article contains additional citation context not shown here]

C. Beeri, R. Ramakrishnan, D. Srivastava, and S. Sudarshan. A proof theoretic approach to semantics for logic programs. Submitted for publication. Parts of the paper appeared in `The Valid Model Semantics for Logic Programs ' (PODS'92), and in `Extending the Well-Founded and Valid Semantics for Aggregation' (ILPS'93)., 1994.

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