Negation and Aggregates in Recursive Rules: the LDL++ Approach

  title={Negation and Aggregates in Recursive Rules: the LDL++ Approach},
  author={Carlo Zaniolo and Natraj Arni and KayLiang Ong},
The problem of allowing non-monotonic constructs, such as negation and aggregates, in recursive programs represents a difficult challenge faced by current research in deductive databases. In this paper, we present a solution that combines generality with efficiency, as demonstrated by its implementation in the new LDL++ system. A novel and general treatment of set aggregates, allowing for user-defined aggregates, is also presented. 
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Data and knowledge in database systems: deductive databases
Deductive database research has produced methods and techniques for implementing the declarative semantics of logical rules via efficient computation of fixpoints, and their techniques have been incorporated into a new generation of commercial databases.
Fixpoint iteration with subsumption in deductive databases
This paper proposes user-supplied subsumption information as a paradigm to specify desired, prefered or useful deductions at the meta level and augment logic programming by subsumption relations and succeeds to extend the classical theorems for least models, fixpoints and bottom-up evaluation accordingly.
Nondeterministic, Nonmonotonic Logic Databases
An extension of Datalog with mechanisms for temporal, nonmonotonic, and nondeterministic reasoning, which is referred to as Datalogy++ is considered and its flexibility in expressing queries concerning aggregates and data cube is shown.
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Recent advances in the semantics of nonmonotonic logic are reviewed and it is shown that they can be used to unify the foundations of active databases and deductive databases.
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This paper considers an extension of Datalog with mechanisms for non-monotonic and non-deterministic reasoning and a simple form of temporal reasoning, which it is shown how with this logic database language is possible to express problems in heterogeneous domains.


Non-Determinism in Deductive Databases
A construct called dynamic choice is defined, which is consistent with the fixpoint-based semantics, cures the deficiencies of the former approach, and leads to efficient implementations in the framework of deductive databases.
Monotonic aggregation in deductive databases
This work forms a minimal model of a program component including aggregate operators, rather than insisting that the aggregate apply to atoms that have been fully determined, or that aggregate functions are rewritten in terms of negation.
Why not negation by fixpoint?
Inflationary DATALOG is proposed, an efficiently implementable semantics for negation, based on inflationary fixpoints, that is a natural generalization of the standard semantics for DATalOG programs without negation.
A Unified Semantics for Active and Deductive Databases
  • C. Zaniolo
  • Computer Science
    Rules in Database Systems
  • 1993
Recent advances in the semantics of non-monotonic logic are reviewed and it is shown that they can be used to unify the foundations of active databases and deductive databases.
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The two most successful semantic approaches to the problem of recursion through negation, well founded models and stable models, are extended to programs with aggregates and there are programs not captured in any previously deened class where the unique stable model agrees with their \intuitive" semantics.
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The stable model semantics for logic programs provides a unified basis for the treatment of negation and non-determinism and it is shown that the maximal deterministic model of a program is a subset of the intersection of all its stable models.
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The well-founded semantics of aggregation
Extensions to the semantics, restrictions on the input, and other supplementary requirements proposed in earlier studies appear to be unnecessary for the purpose of attaching a meaning to a program that involves recursion through aggregation.