Processing negation and disjunction in logic programs through integrity constraints

Integrity constraints were initially defined to verify the correctness of the data that is stored in a database. They were used to restrict the modifications that can be applied to a database. However, there are many other applications in which integrity constraints can play an important role. For example, the semantic query optimization method developed by Chakravarthy, Grant, and Minker for definite deductive databases uses integrity constraints during query processing to prevent the exploration of search space that is bound to fail. In this paper, we generalize the semantic query optimization method to apply to negated atoms. The generalized method is referred to assemantic compilation. This exploration has led to two significant results. First, semantic compilation provides an alternative search space for negative query literals. The alternative search space can find answers in cases for which negation-as-finite-failure and constructive negation cannot. Second, we show how semantic compilation can be used to transform a disjunctive database with or without functions and denial constraints without negation into a new disjunctive database that complies with the integrity constraints.     

Duality for Goal-Driven Query Processing in Disjunctive Deductive Databases

Bottom-up query-answering procedures tend to explore a much larger search space than what is strictly needed. Top-down processing methods use the query to perform a more focused search that can result in more efficient query answering. Given a disjunctive deductive database, DB, and a query, Q, we establish a strong connection between model generation and clause derivability in two different representations of DB and Q. This allows us to use a bottom-up procedure for evaluating Q against DB in a top-down fashion. The approach requires no extensive rewriting of the input theory and introduces no new predicates. Rather, it is based on a certain duality principle for interpreting logical connectives. The duality transformation is achieved by reversing the direction of implication arrows in the clauses representing both the theory and the negation of the query. The application of a generic bottom-up procedure to the transformed clause set results in top-down query answering. Under favorable conditions efficiency gains are substantial, as shown by our preliminary testing. We give the logical meaning of the duality transformation and point to the conditions and sources of improved efficiency. We show how the duality approach can be used for refined query answering by specifying the minimal conditions (weakest updates) to DB under which Q becomes derivable. This is shown to be useful for view updates in disjunctive deductive databases as well as for other interesting applications.     

Minimal model generation for refined answering of generalized queries in disjunctive deductive databases

Generalized queries are defined as sets of clauses in implication form. They cover several tasks of practical importance for database maintenance such as answering positive queries, computing database completions and integrity constraints checking. We address the issue of answering generalized queries under the minimal model semantics for the class of disjunctive deductive databases (DDDBs). The advanced approach is based on having the query induce an order on the models returned by a sound and complete minimal model generating procedure. We consider answers that are true in all and those that are true in some minimal models of the theory. We address the issue of answering positive queries through the construction of the minimal model state of the DDDB, using a minimal model generating procedure. The refinements allowed by the procedure include isolating a minimal component of a disjunctive answer, the specification of possible updates to the theory to enable the derivability of certain queries and deciding the monotonicity properties of answers to different classes of queries.     

Query evaluation in recursive databases: bottom-up and top-down reconciled

It is desirable to answer queries posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up processing — the naive and semi-naive methods — are rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new fixpoint procedure that performs a different kind of reasoning: We specify a top-down query answering method, which we call the Backward Fixpoint Procedure. Then, we reconsider query evaluation methods for recursive databases. First, we show that the methods based on rewriting on the one hand, and the methods based on resolution on the other hand, implement the Backward Fixpoint Procedure. Second, we interpret the rewritings of the Alexander and Magic Set methods as specializations of the Backward Fixpoint Procedure. Finally, we argue that such a rewriting is also needed in a database context for implementing efficiently the resolution-based methods. Thus, the methods based on rewriting and the methods based on resolution implement the same top-down evaluation of the original database rules by means of auxiliary rules processed bottom-up.     

Extending Datalog with Declarative Updates

The semantics of static deductive databases is well understood based on the work in logic programming. In the past decade, various methods to incorporate update constructs into logic programming and deductive databases have been proposed. However, there is still no consensus about the appropriate treatment of dynamic behavior in deductive databases. In this paper, we propose a language called DatalogU, which is a minimal but powerful extension of Datalog with updates to base relations. DatalogU allows the user to program set-oriented complex database transactions with concurrent, disjunctive and sequential update operations in a simple and direct way. It has a simple and intuitive declarative semantics that naturally accounts for set-oriented updates in deductive databases.     

Chain-split evaluation in deductive databases

Many popularly studied recursions in deductive databases can be compiled into one or a set of highly regular chain generating paths, each of which consists of one or a set of connected predicates. Previous studies on chain-based query evaluation in deductive databases take a chain generating path as an inseparable unit in the evaluation. However, some recursions, especially many functional recursions whose compiled chain consists of infinitely evaluable function(s), should be evaluated by chain-split evaluation, which splits a chain generating path into two portions in the evaluation: an immediately evaluable portion and a delayed-evaluation portion. The necessity of chain-split evaluation is examined from the points of view of both efficiency and finite evaluation, and three chain-split evaluation techniques: magic sets, buffered evaluation, and partial evaluation are developed. Our study shows that chain-split evaluation is a primitive recursive query evaluation technique for different kinds of recursions, and it can be implemented efficiently in deductive databases by extensions to the existing recursive query evaluation methods     

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.Research supported in part by NSF under IRI-9210220 and IRI-9111988, Omron Corporation and Omron Management Center of America.     

Relaxation as a platform for cooperative answering

Responses to queries posed by a user of a database do not always contain the information desired. Database answers to a query, although they may be logically correct, can sometimes be misleading. Research in the area of cooperative answering for databases and deductive databases seeks to rectify these problems. We introduce a cooperative method calledrelaxation for expanding deductive database and logic programming queries. The relaxation method expands the scope of a query by relaxing the constraints implicit in the query. This allows the database to return answers related to the original query as well as the literal answers themselves. These additional answers may be of interest to the user. In section 1 we introduce the problem and method. In Section 2 we give some background on the research done in cooperative answering. Section 3 discusses the relaxation method, a potential control strategy, and uses. Section 4 looks at a semantic counterpart to this notion. In Section 5 we explore some of the control and efficiency issues. We enumerate open issues in Section 6, and conclude in Section 7.     

A database of groups of prime-power order

The design, implementation and performance of TwoGroups, a deductive database for the 58,761 groups of order 2ⁿ, (n ≤ 8), is described. The system is implemented in NU-Prolog, a Prolog system with built-in functions for creating and using deductive databases. TwoGroups has a set-theoretic query language, which provides users with a familiar notation to access the data. The paper describes the data and its representation, the set-theoretic query language, its translator and optimiser, and the experiments on the performance of the database.     

Constraint-based query evaluation in deductive databases

Constraints play an important role in the efficient query evaluation in deductive databases. Constraint-based query evaluation in deductive databases is investigated, with emphasis on linear recursions with function symbols. Constraints are grouped into three classes: rule constraints, integrity constraints, and query constraints. Techniques are developed for the maximal use of different kinds of constraints in rule compilation and query evaluation. The study on the roles of different classes of constraints in set-oriented evaluation of linear recursions shows the following: rule constraints should be integrated with their corresponding deduction rules in the compilation of recursions; integrity constraints, including finiteness constraints and monotonicity constraints, should be used in the analysis of finite evaluability and termination for specific queries; and query constraints, which are often useful in search space reduction and termination, should be transformed, when necessary, and should be pushed into the compiled chains as deeply as possible for efficient evaluation. The constraint-based query-processing technique integrates query-independent compilation and chain-based query evaluation methods and demonstrates its great promise in deductive query evaluation