Deductive databases with conditional facts

The problem of determining the correct declarative semantics for generalized logic programs is still open. In generalized logic programs the body of a rule may contain negated goals. Using a logical equivalence these programs may be viewed as disjunctive logic programs where the head of a rule may contain a disjunction of goals. We hope that a careful study of the declarative semantics of disjunctive logic programs will produce criteria for evaluating the different candidates for the semantics of generalized logic programs.A conceptual analysis leads to a semantical definition of the notion of a disjunctive deductive database as a generalization of the notion of a deductive database. It will be shown that the notion of a disjunctive deductive database is equivalent to the syntactical definition of a disjunctive logic program. We have characterized disjunctive deductive databases, i. e. theories which admit in each irreducible component a minimal Herbrand model and for which this property is preserved under the addition of new facts, as disjunctive logic programs. As a special case the result yields the known characterization of deductive databases, i. e. theories which admit a minimal Herbrand model and for which this property is preserved under the addition of new facts, as logic programs. In the presence of equations term structures i. e. extended Herbrand structures replace the Herbrand structures and h-core models replace the minimal models. Actually, the results could be proved in a more general context where pseudo term structures replace the term structures. In addition, there is an intermediate case where the irreducible components coincide with the connected components. Moreover, there are characterization results for the cases where the uniformity condition is not present.KeywordsLogic ProgramIrreducible ComponentTerm StructureCanonical ModelDeductive DatabaseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A review is presented of work on disjunctive deductive databases. The semantic approach to disjunctive deductive databases as developed by Fernandez and Minker is explored. The method is applied to stratified and stable model semantics for disjunctive deductive databases. The semantics for updating a subclass of disjunctive deductive databases is described.

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.

In this paper a set-oriented bottom-up parsing system based on a deductive database is presented. The system allows the purely declarative specification of Definite Clause Grammar rules as a logic program. The parser applies a set-oriented bottom-up evaluation strategy. It is therefore particularly wellsuited for the analysis of language ambiguities. Furthermore the system can easily be connected to a relational database. The impedance mismatch between a tuple-oriented PROLOG system and a set-oriented relational database system is avoided. Thus a number of drawbacks which PROLOG based parsers suffer from have been overcome.

Traditional database query languages such as datalog and SQL allow the user to specify only mandatory requirements on the data to be retrieved from a database. In many applications, it may be natural to express not only mandatory requirements but also preferences on the data to be retrieved. Lacroix and Lavency10) extended SQL with a notion of preference and showed how the resulting query language could still be translated into the domain relational calculus. We explore the use of preference in databases in the setting of datalog. We introduce the formalism of preference datalog programs (PDPs) as preference logic programs without uninterpreted function symbols for this purpose. PDPs extend datalog not only with constructs to specify which predicate is to be optimized and the criterion for optimization but also with constructs to specify which predicate to be relaxed and the criterion to be used for relaxation. We can show that all of the soft requirements in Reference10) can be directly encoded in PDP. We first develop anaively-pruned bottom-up evaluation procedure that is sound and complete for computing answers to normal and relaxation queries when the PDPs are stratified, we then show how the evaluation scheme can be extended to the case when the programs are not necessarily stratified, and finally we develop an extension of themagic templates method for datalog14) that constructs an equivalent but more efficient program for bottom-up evaluation.

In this paper we present the set-oriented bottom-up parsing system AMOS which is a major application of the LOLA deductive database system. AMOS supports the morpho-syntactical analysis of Old Hebrew and has now been operationally used by linguists for a couple of years. The system allows the declarative specification of Definite Clause Grammar rules. Due to the set-oriented bottom-up evaluation strategy of LOLA LOLA it is particularly well suited to the analysis of language ambiguities.

Argumentation-based abduction in disjunctive logic programming

On the equivalence of the static and disjunctive well-founded semantics and its computation

This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the well-known Magic-Set technique and is well-suited for being integrated in current bottom-up (stable) model inference engines. More specifically, it is based on the exploitation of binding propagation techniques which reduce the size of the data relevant to answer the query and, consequently, reduces both the complexity of computing a single model and the number of models to be considered. The motivation of this work stems from the observation that traditional binding propagation optimization techniques for bottom-up model generator systems, simulating the goal driven evaluation of top-down engines, are only suitable for positive (disjunctive) queries, while hard problems are expressed using unstratified negation. The main contribution of the paper consists in the extension of a previous technique, defined for positive disjunctive queries, to queries containing both disjunctive heads and constraints (a simple and expressive form of unstratified negation). As the usual way of expressing declaratively hard problems is based on the guess-and-check technique, where the guess part is expressed by means of disjunctive rules and the check part is expressed by means of constraints, the technique proposed here is highly relevant for the optimization of queries expressing hard problems. The value of the technique has been proved by several experiments.

We are proposing a keyword-based query interface for knowledge bases - including relational or deductive databases - based on contextual background knowledge such as suitable join conditions or synonyms. Join conditions could be extracted from existing referential integrity (foreign key) constaints of the database schema. They could also be learned from other, previous database queries, if the database schema does not contain foreign key constraints.
\nGiven a textual representation - a word list - of a query to a relational database, one may parse the list into a structured term. The intelligent and cooperative part of our approach is to hypothesize the semantics of the word list and to find suitable links between the concepts mentioned in the query using contextual knowledge, more precisely join conditions between the database tables.
\nWe use a knowledge-based parser based on an extension of Definite Clause Grammars (Dcg) that are interweaved with calls to the database schema to suitably annotate the tokens as table names, table attributes, attribute values or relationships linking tables. Our tool DdQl yields the possible queries in a special domain specific rule language that extends Datalog, from which the user can choose one.

Possible Model Semantics for Disjunctive Databases

When processing a query in a conventional database a set of facts are usually returned for an answer. This can be different in a deductive or expert database system. Users may, as before, be interested in a set of facts to answer their query, but in certain queries users are also able to get the answer of a query as a set of formulas (e.g., facts, intensional answers).

We study conditions guaranteeing polynomial time computability of queries in temporal deductive databases. We show that if for a given set of temporal rules, the period of its least models is bounded from the above by a polynomial in the database size, then also the time to process yes-no queries (as well as to compute finite representations of all query answers) can be polynomially bounded. We present a bottom-up query processing algorithm BT that is guaranteed to terminate in polynomial time if the periods are polynomially bounded. Polynomial periodicity is our most general criterion, however it can not be directly applied. Therefore, we exhibit two weaker criteria, defining inflationary and I-periodic sets of temporal rules. We show that it can be decided whether a set of temporal rules is inflationary. I-periodicity is undecidable (as we show), but it can be closely approximated by a syntactic notion of multi-separability.

A Prolog-based experimental system for relational databases that is not defined from the viewpoint of any specific relational topic is proposed. The idea is that the experimental system can be used in many different contexts such as query optimization, data restructuring and database design. The definition is based entirely on the theoretical foundations of the relational model. The experimental system offers a well-defined environment for studying how other systems can be integrated with relational databases. The use of the experimental system in the context of different approaches to deductive databases is considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The need for representing indefinite information led to disjunctive deductive databases, which also fertilized work on disjunctive logic programming. Base on this paradigm, the DLV system has been designed and implemented as a tool for declarative knowledge representation. In this paper, we focus on the usage of DLV for solving problems in a declarative manner and report on experiments that we have run on a suite of benchmark problems. We discuss how problems can be solved in a natural way using a "Guess&Check"-paradigm where solutions are guessed and verified by parts of the program. Furthermore, we describe various front-ends that can be used for solving problems in specific applications. The experiments show that due to the ongoing implementation efforts, which include fine -tuning of the underlying algorithms, successive and significant performance improvements have been achieved during the last two years. The results indicate that DLV is capable of solving some complex problems quite efficiently.