4,370 research outputs found
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
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
A Rational and Efficient Algorithm for View Revision in Databases
The dynamics of belief and knowledge is one of the major components of any
autonomous system that should be able to incorporate new pieces of information.
In this paper, we argue that to apply rationality result of belief dynamics
theory to various practical problems, it should be generalized in two respects:
first of all, it should allow a certain part of belief to be declared as
immutable; and second, the belief state need not be deductively closed. Such a
generalization of belief dynamics, referred to as base dynamics, is presented,
along with the concept of a generalized revision algorithm for Horn knowledge
bases. We show that Horn knowledge base dynamics has interesting connection
with kernel change and abduction. Finally, we also show that both variants are
rational in the sense that they satisfy certain rationality postulates stemming
from philosophical works on belief dynamics
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
Variations on a Theme: A Bibliography on Approaches to Theorem Proving Inspired From Satchmo
This articles is a structured bibliography on theorem provers,
approaches to theorem proving, and theorem proving applications inspired
from Satchmo, the model generation theorem prover developed
in the mid 80es of the 20th century at ECRC, the European Computer-
Industry Research Centre. Note that the bibliography given in this article
is not exhaustive
A New Rational Algorithm for View Updating in Relational Databases
The dynamics of belief and knowledge is one of the major components of any
autonomous system that should be able to incorporate new pieces of information.
In order to apply the rationality result of belief dynamics theory to various
practical problems, it should be generalized in two respects: first it should
allow a certain part of belief to be declared as immutable; and second, the
belief state need not be deductively closed. Such a generalization of belief
dynamics, referred to as base dynamics, is presented in this paper, along with
the concept of a generalized revision algorithm for knowledge bases (Horn or
Horn logic with stratified negation). We show that knowledge base dynamics has
an interesting connection with kernel change via hitting set and abduction. In
this paper, we show how techniques from disjunctive logic programming can be
used for efficient (deductive) database updates. The key idea is to transform
the given database together with the update request into a disjunctive
(datalog) logic program and apply disjunctive techniques (such as minimal model
reasoning) to solve the original update problem. The approach extends and
integrates standard techniques for efficient query answering and integrity
checking. The generation of a hitting set is carried out through a hyper
tableaux calculus and magic set that is focused on the goal of minimality.Comment: arXiv admin note: substantial text overlap with arXiv:1301.515
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