Disjunctive Deductive Databases Research Articles

Dynamic maintenance of the transitive closure in disjunctive graphs

We propose an approach with feasible space requirement to maintain the transitive closure of a class of hypergraphs called OR-graphs. OR-graphs are equivalent to disjunctive deductive databases where disjunctions are limited to one attribute in each OR-table. It has been shown that query processing in disjunctive deductive databases grows into CoNP with very simple examples, but few attempts have been made, as is done in this paper, to obtain classes of disjunctive databases and queries for which efficient algorithms exist. Polynomial time algorithms are presented to compute the transitive closure of OR-graphs and to handle dynamic insertions and deletions. With algorithms for insertions and deletions, we provide a simple but efficient technique to solve the failure set problem in reliability models, which is equivalent to finding the closure of an arbitrary non-empty set of simple nodes. We also show that a minimal extension to OR-graphs makes the computational complexity of the transitive closure CoNP-complete.

COMPUTING PERFECT AND STABLE MODELS USING ORDERED MODEL TREES

Ordered model trees were introduced as a normal form for disjunctive deductive databases. They were also used to facilitate the computation of minimal models for disjunctive theories by exploiting the order imposed on the Herbrand base of the theory. In this work we show how the order on the Herbrand base can be used to compute perfect models of a disjunctive stratified finite theory. We are able to compute the stable models of a general finite theory by combining the order on the elements of the Herbrand base with previous results that had shown that the stable models of a theory T can be computed as the perfect models of a corresponding disjunctive theory ɛT resulting from applying the so called evidential transformation to T. While other methods consider many models that are rejected at the end, the use of atom ordering allows us to guarantee that every model generated belongs to the class of models being computed. As for negation‐free databases, the ordered tree serves as the canonical representation of the database.

QUERY EVALUATION IN PARTITIONED DISJUNCTIVE DEDUCTIVE DATABASES

Query evaluation in disjunctive deductive databases is in general computationally hard. The class of databases for which the process is tractable is severely limited. The complexity of the process depends on the structure of the database as well as on the type of query being evaluated. In this paper we study the issue of simplified query processing in disjunctive deductive databases. We address the possibility of evaluating general queries by independently processing their atomic components and describe the class of databases for which this approach is possible. We also discuss the issue of dividing a disjunctive deductive database into a set of disjoint components then answering queries and computing database completions by combining the results obtained against the individual components. Some practical special cases are considered. The methods developed in this paper can be utilized to introduce parallelism into the query evaluation process.

Ordered model trees: A normal form for disjunctive deductive databases

Model trees were conceived as a structure-sharing approach to represent information in disjunctive deductive databases. In this paper we introduce the concept ofordered minimal model trees as a normal form for disjunctive deductive databases. These are model trees in which an order is imposed on the elements of the Herbrand base. The properties of ordered minimal model trees are investigated as well as their possible utilization for efficient manipulation of disjunctive deductive databases. Algorithms are presented for constructing and performing operations on ordered model trees. The complexity of ordered model tree processing is addressed. Model forests are presented as an approach to reduce the complexity of ordered model tree construction and processing.