Optimization of bound disjunctive queries with constraints

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.

We introduce the notion of conditional facts in deductive databases. The language used to express the conditions in the basic facts does not involve constructs used to describe the database and is motivated by its potential usefulness in expressing disjunctive facts and answering queries in disjunctive deductive databases. We present a bottom-up procedure that uses tabular structures to represent the conditional facts and computes the intended meaning of conditional deductive databases. We show how this procedure can be used to answer queries in a subclass of disjunctive deductive databases which involves disjunctive facts but only definite rules.

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.

Argumentation-based abduction in disjunctive logic programming

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

Logic programs, deductive databases, and more generally non-monotonic theories, use various forms of default negation, not F , whose major distinctive feature is that not F is assumed “by default”, i.e., it is assumed in the absence of sufficient evidence to the contrary. The meaning of “sufficient evidence” depends on the specific semantics used. For example, in Reiter’s Closed World Assumption, CWA [32], not A is assumed for atomic A if A is not provable, or, equivalently, if there is a minimal model in which A is false. On the other hand, in Minker’s Generalized Closed World Assumption, GCWA [18, 16], or in McCarthy’s Circumscription, CIRC [17], not A is assumed only if A is false in all minimal models. In Clark’s Predicate Completion semantics for logic programs [7], this form of negation is called negation-as-failure because not A is derivable whenever attempts to prove A finitely fail. The more recent semantics proposed for logic programs and deductive databases, such as the stable semantics [14], well-founded semantics [34], partial stable or stationary semantics [27] and static semantics [30], propose even more sophisticated meanings for default negation, closely related to more general nonmonotonic formalisms such as Default Logic, DL [33], AutoEpistemic Logic, AEL [19], and AutoEpistemic logic of Beliefs, AEB [29]. Under all of these semantics, however, default negation “not ” significantly differs from classical negation “¬”. For example, the formula charged(x) ∧ ¬guilty(x) ⊃ acquitted(x) says that a person charged with a crime should be acquitted if he or she is actually proven to be not guilty. On the other hand, the formula charged(x) ∧ not guilty(x) ⊃ acquitted(x) says that one should be acquitted of any charges by default unless sufficient evidence of that person’s guilt is demonstrated.

This work discusses a novel approach, Bayesian-inspired multifidelity optimization, for solving complex optimization requiring computationally expensive simulations. Bayesian-inspired multifidelity optimization aims to minimize computational cost in achieving accurate high-fidelity results through the use of low-fidelity (computationally cheaper) models in combination with a surrogate correction model. A novel Bayesian hybrid bridge function was developed to serve as the low-fidelity correction technique. This Bayesian hybrid bridge function is a Bayesian weighted average of two standard bridge functions, additive and multiplicative. The correction technique is implemented in parallel with a modified trust region model management optimization scheme. It is shown that optimization on the corrected low-fidelity model converges to the same local optimum as optimization on the high-fidelity model in fewer high-fidelity model. This technique is developed to reach that optimum in fewer high-fidelity function evaluations than traditional optimization, ultimately reducing computational cost. This work also extends the low-fidelity correction optimization beyond the traditional bifidelity optimization to that of optimization with multiple-fidelity objective and constraint functions. The proposed solution technique allows for use of commercial optimizers and is demonstrated on three separate problems. The first demonstration is on a one-dimensional analytical test case in which the Bayesian correction is shown. Then, the ability to handle multiple fidelities in both the objective and constraint functions is presented and discussed using a two-dimensional analytical test case. An airfoil shape optimization problem is then used to illustrate the effectiveness of this approach in an engineering design scenario in which the various fidelities arise as a difference in computational physics. It is shown via these demonstrations that implementation of this Bayesian low-fidelity correction optimization approach results in convergence to a high-fidelity optimum at a reduced computational cost in comparison to traditional optimization techniques.

A crucial challenge for global query optimization in a multidatabase system (MDBS) is that some local optimization information, such as local cost parameters, may not be accurately known at the global level because of local autonomy. Traditional query optimization techniques using a crisp cost model may not be suitable for an MDBS because precise information is required. In this paper we present a new approach that performs global query optimization using a fuzzy cost model that allows fuzzy information. We suggest methods for establishing a fuzzy cost model and introduce a fuzzy optimization criterion that can be used with a fuzzy cost model. We discuss the relationship between the fuzzy optimization approach and the traditional (crisp) optimization approach and show that the former has a better chance to find a good execution strategy for a query in an MDBS environment, but its complexity may grow exponentially compared with the complexity of the later. To reduce the complexity, we suggest to use so-called k-approximate fuzzy values to approximate all fuzzy values during fuzzy query optimization. It is proven that the improved fuzzy approach has the same order of complexity as the crisp approach.

In this paper, we study the problem of query rewriting for disjunctive existential rules. Query rewriting is a well-known approach for query answering on knowledge bases with incomplete data. We propose a rewriting technique that uses negative constraints and conjunctive queries to remove the disjunctive components of disjunctive existential rules. This process eventually generates new non-disjunctive rules, i.e., existential rules. The generated rules can then be used to produce new rewritings using existing rewriting approaches for existential rules. With the proposed technique we are able to provide complete UCQ-rewritings for union of conjunctive queries with universally quantified negation. We implemented the proposed algorithm in the Completo system and performed experiments that evaluate the viability of the proposed solution.

Evolutionary algorithms, simulated annealing and tabu search: a comparative study

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding--to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that stable models of a safe sentence can be characterized by a formula of a simple syntactic form.

Traditional query optimizers rely on the accuracy of estimated statistics of intermediate subexpressions to choose good query execution plans. This design often leads to suboptimal plan choices for complex queries since errors in estimates grow exponentially in the presence of skewed and correlated data distributions. We propose to demonstrate the Rio prototype database system that uses proactive re-optimization to address the problems with traditional optimizers. Rio supports three new techniques:1. Intervals of uncertainty are considered around estimates of statistics during plan enumeration and costing2. These intervals are used to pick execution plans that are robust to deviations of actual values of statistics from estimated values, or to defer the choice of execution plan until the uncertainty in estimates can be resolved3. Statistics of intermediate subexpressions are collected quickly, accurately, and efficiently during query executionThese three features are fully functional in the current Rio prototype which is built using the Predator open-source DBMS [5]. In this proposal, we first describe the novel features of Rio, then we use an example query to illustrate the main aspects of our demonstration.

Since the era of big data, enhancement of the speed of the database query is the critical problem. Fundamental part of any database management system is query optimizer. So, it should be able to choose the suitable search strategy which can give quicker response even with complex and large amount of data. The expansion of database application areas, where a query may include more than 100 joins, traditional query optimization techniques, i.e., greedy-based optimization and dynamic programming unable to find the solution but its observed from the metaheuristic algorithm like genetic algorithms (GA), particle swarm optimization (PSO) and ant colony optimization (ACO) algorithms gives optimal solution. These algorithms do not guarantee the best optimal solution, rather near best solution, which is tolerable. However, there is the limitation of slow convergence and high computation effort in GA and stagnation with premature convergence in ACO. Therefore, we proposed the hybridization of our modified ACO with GA to overcome the above limitations for multi-join query optimization and experimentally shown our proposed method on randomly created dataset gives better results over GA and ACO in terms of distance and execution times.

In last 30 years, effectiveness of ES algorithms has induced many people to believe that they are the methods of choice for hard real-life problems superseding traditional search techniques. However, they are not without their limitations. In particular, the choice of a good evolutionary operator can make a considerable difference to the exploration and exploitation, and often even the feasibility of the evolutionary search. Moreover, the success and progress of an evolutionary search algorithm mostly depends upon the balance between population diversity and selective pressure [97]. To meet these requirements, contemporary ESs [11, 15, 110, 124, 16, 17] usually apply self-adaptation in so-called strategy parameters (or internal model) of the object variables. While optimizing the objective function, the self-adaptation technique requires optimization of the strategy parameters as well [108]. This dual optimization creates algorithmic complexity and in turn, it causes expense in computation time. Regarding this, Back et al. [17][p.7] stated as The amount of information included into the individuals by means of the self-adaptation principle increases from the simple case of one standard deviation up to the order of n2 additional parameters, which reflects an enormous degree offreedom for the internal models of the individuals. This growing degree offreedom often enhances the global search capabilities of the algorithm at the cost of the expense in computation time, and...