393 research outputs found
Query Evaluation in Deductive Databases
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
Upside-down Deduction
Over the recent years, several proposals were made to enhance database systems with automated reasoning. In this article we analyze two such enhancements based on meta-interpretation. We consider on the one hand the theorem prover Satchmo, on the other hand the Alexander and Magic Set methods. Although they achieve different goals and are based on distinct reasoning paradigms, Satchmo and the Alexander or Magic Set methods can be similarly described by upside-down meta-interpreters, i.e., meta-interpreters implementing one reasoning principle in terms of the other. Upside-down meta-interpretation gives rise to simple and efficient implementations, but has not been investigated in the past. This article is devoted to studying this technique. We show that it permits one to inherit a search strategy from an inference engine, instead of implementing it, and to combine bottom-up and top-down reasoning. These properties yield an explanation for the efficiency of Satchmo and a justification for the unconventional approach to top-down reasoning of the Alexander and Magic Set methods
Transformation-Based Bottom-Up Computation of the Well-Founded Model
We present a framework for expressing bottom-up algorithms to compute the
well-founded model of non-disjunctive logic programs. Our method is based on
the notion of conditional facts and elementary program transformations studied
by Brass and Dix for disjunctive programs. However, even if we restrict their
framework to nondisjunctive programs, their residual program can grow to
exponential size, whereas for function-free programs our program remainder is
always polynomial in the size of the extensional database (EDB).
We show that particular orderings of our transformations (we call them
strategies) correspond to well-known computational methods like the alternating
fixpoint approach, the well-founded magic sets method and the magic alternating
fixpoint procedure. However, due to the confluence of our calculi, we come up
with computations of the well-founded model that are provably better than these
methods.
In contrast to other approaches, our transformation method treats magic set
transformed programs correctly, i.e. it always computes a relevant part of the
well-founded model of the original program.Comment: 43 pages, 3 figure
Constrained Query Answering
Traditional answering methods evaluate queries only against positive
and definite knowledge expressed by means of facts and deduction rules. They do
not make use of negative, disjunctive or existential information. Negative or indefinite
knowledge is however often available in knowledge base systems, either as
design requirements, or as observed properties. Such knowledge can serve to rule out
unproductive subexpressions during query answering. In this article, we propose an
approach for constraining any conventional query answering procedure with general,
possibly negative or indefinite formulas, so as to discard impossible cases and to
avoid redundant evaluations. This approach does not impose additional conditions
on the positive and definite knowledge, nor does it assume any particular semantics
for negation. It adopts that of the conventional query answering procedure it
constrains. This is achieved by relying on meta-interpretation for specifying the
constraining process. The soundness, completeness, and termination of the underlying
query answering procedure are not compromised. Constrained query answering
can be applied for answering queries more efficiently as well as for generating more
informative, intensional answers
Algebraic optimization of recursive queries
Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud
\ud
In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud
\ud
The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems
Logic Programming as Constructivism
The features of logic programming that
seem unconventional from the viewpoint of classical logic
can be explained in terms of constructivistic logic. We
motivate and propose a constructivistic proof theory of
non-Horn logic programming. Then, we apply this formalization
for establishing results of practical interest.
First, we show that 'stratification can be motivated in a
simple and intuitive way. Relying on similar motivations,
we introduce the larger classes of 'loosely stratified' and
'constructively consistent' programs. Second, we give a
formal basis for introducing quantifiers into queries and
logic programs by defining 'constructively domain
independent* formulas. Third, we extend the Generalized
Magic Sets procedure to loosely stratified and constructively
consistent programs, by relying on a 'conditional
fixpoini procedure
A Review of integrity constraint maintenance and view updating techniques
Two interrelated problems may arise when updating a database. On one
hand, when an update is applied to the database, integrity constraints
may become violated. In such case, the integrity constraint maintenance
approach tries to obtain additional updates to keep integrity
constraints satisfied. On the other hand, when updates of derived or
view facts are requested, a view updating mechanism must be applied to
translate the update request into correct updates of the underlying base
facts.
This survey reviews the research performed on integrity constraint
maintenance and view updating. It is proposed a general framework to
classify and to compare methods that tackle integrity constraint
maintenance and/or view updating. Then, we analyze some of these methods
in more detail to identify their actual contribution and the main
limitations they may present.Postprint (published version
- …