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Efficient consistency control in deductive databases
Abstract
In this paper a theoretical framework for efficiently checking the consistency of deductive databases is provided and proven to be correct. Our method is based on focussing on the relevant parts of the database by reasoning forwards from the updates of a transaction, and using this knowledge about real or just possible implicit updates for simplifying the consistency constraints in question. Opposite to the algorithms by Kowalski/Sadri and Lloyd/Topor, we are neither committed to determine the exact set of implicit updates nor to determine a fairly large superset of it by only considering the head literals of deductive rule clauses. Rather, our algorithm unifies these two approaches by allowing to choose any of the above or even intermediate strategies for any step of reasoning forwards. This flexibility renders possible the integration of statistical data and knowledge about access paths into the checking process. Second, deductive rules are organized into a graph to avoid searching for applicable rules in the proof procedure. This graph resembles a connection graph, however, a new method of interpreting it avoids the introduction of new clauses and links.
... The derivation of safe insertions and potential deletions is proposed, e.g., in [23, 37] . Calculating induced updates in different granularities has already been proposed by Moerkotte and Karl in [28], restricted to positive databases, though. The propagation rules proposed in this paper are restricted to the propagation of insertions and deletions of base facts in stratifiable databases. ...
We investigate the possibility to use update propagation methods for optimizing the evaluation of continuous queries. Update propagation allows for the efficient determination of induced changes to derived relations resulting from an explicitly performed base table update. In order to simplify the computation process, we propose the propagation of updates with different degrees of granularity which corresponds to an incremental query evaluation with different levels of accuracy. We show how propagation rules for different update granularities can be systematically derived, combined and further optimized by using Magic Sets. This way, the costly evaluation of certain subqueries within a continuous query can be systematically circumvented allowing for cutting down on the number of pipelined tuples considerably.
Recent years have witnessed a continuous evolution of database models towards richer and more expressive paradigms. Along the line of enriching the modeling capabilities, Object-Oriented databases (OODBs) have been introduced. In this paper, we propose a further enhancement to OODB models aiming at enriching the database schema by explicitly declaring semantic integrity constraints therein.
In the paper, we present an Object-Oriented data definition language, referred to as TQL. It allows the construction of an OODB schema using the well known data structuring mechanisms, such as NF2 attributes, complex types, and multiple inheritance in class (type) hierarchies. In addition, TQL allows the further enrichment of the schema by expressing explicit integrity constraints. The proposal includes the definition of the formal semantics of TQL, according to a denotational approach, and the notion of correctness of schemas, with particular emphasis on the legality of ISA hierarchies. The proposed language is the basis of the prototype MOSAICO, an environment for the design and rapid prototyping of OODB applications developed at IASI.
An update of a consistent database can influence the integrity of the database. The available integrity checking methods in deductive databases are often criticized for their lack of efficiency. The main goal of this paper is to present a new integrity checking method which does not have some of the disadvantages of existing methods. The main advantage of the proposed method is that the integrity check is performed primarily at compile time. In order to demonstrate the improvement in efficiency of the proposed method it was compared both fundamentally and experimentally with existing methods.
Bonn, University, Diss., 2004 (Nicht für den Austausch).
We describe the theory and implementation of a general theorem-proving technique for checking integrity of deductive databases recently proposed by Sadri and Kowalski. The method uses an extension of the SLDNF proof procedure and achieves the effect of the simplification algorithms of Nicolas, Lloyd, Topor et al, and Decker by reasoning forwards from the update and thus focusing on the relevant parts of the database and the relevant constraints.
Various deficiencies of resolution systems are investigated and a new theorem-proving system designed to remedy those deficiencms is presented The system is notable for eliminating re- dundancies present in SL-resolutlon, for incorporating preprocessing procedures, for liberahzing the order in which subgoals can be activated, for incorporating multidirectmnal searches, and for giving immediate access to pairs of clauses which resolve Examples of how the new system copes with the defic2encies of other theorem-proving systems are chosen from the areas of predicate logic program- ming and language parsing. The paper emphasizes the historical development of the new system, beginning as a supplement to SL-resolution in the form of classificatmn trees and incorporating an analogue of the Waltz algorithm for picture Interpretation The paper ends with a discussion of the opportunities for using look-ahead to guide the search for proofs
This paper provides a theoritical basis for deductive database systems. A deductive database consists of closed typed first order logic formulas of the form A ← W, where A is an atom and W is a typed first order formula. A typed first order formula can be used as a query, and a closed typed first order formula can be used as an integrity constraint. Functions are allowed to appear in formulas. Such a deductive database system can be implemented using a PROLOG system. The main results are the soundness of the query evaluation process, the soundness of the implementation of integrity constraints, and a simplification theorem for implementing integrity constraints. A short list of open problems is also presented.
Deductive question-answering systems generally evaluate queries under one of two possible assumptions which we in this paper refer to as the open and closed world assumptions. The open world assumption corresponds to the usual first order approach to query evaluation: Given a data base DB and a query Q, the only answers to Q are those which obtain from proofs of Q given DB as hypotheses. Under the closed world assumption, certain answers are admitted as a result of failure to find a proof. More specifically, if no proof of a positive ground literal exists, then the negation of that literal is assumed true.
In this paper, we show that closed world evaluation of an arbitrary query may be reduced to open world evaluation of so-called atomic queries. We then show that the closed world assumption can lead to inconsistencies, but for Horn data bases no such inconsistencies can arise. Finally, we show how for Horn data bases under the closed world assumption purely negative clauses are irrelevant for deductive retrieval and function instead as integrity constraints.
When an "updating" operation occurs on the current state of a data base, one has to ensure the new state obeys the integrity constraints. So, some of them have to be evaluated on this new state. The evaluation of an integrity constraint can be time consuming, but one can improve such an evaluation by taking advantage from the fact that the integrity constraint is satisfied in the current state. Indeed, it is then possible to derive a simplified form of this integrity constraint which is sufficient to evaluate in the new state in order to determine whether the initial constraint is still satisfied in this new state. The purpose of this paper is to present a simplification method yielding such simplified forms for integrity constraints. These simplified forms depend on the nature of the updating operation which is the cause of the state change. The operations of inserting, deleting, updating a tuple in a relation as well as transactions of such operations are considered. The proposed method is based on syntactical criteria and is validated through first order logic. Examples are treated and some aspects of the method application are discussed.