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We introduce a general method for paraconsistent reasoning in knowledge systems by classical second-order formulae. A standard technique for paraconsistent reasoning on inconsistent classical theories is by shifting to multiple-valued logics. We show how these multiple-valued theories can be “shifted back” to two-valued classical theories (through a polynomial transformation), and how preferential...
We have shown elsewhere how to introduce a concept of syntactic unification when terms are taken as the elements in a free module. This is done so as to obtain an m.g.u and its uniqueness modulo isomorphism. Here we introduce the concept of an implementation: An injective function from a term algebra into another object in a different category, both free over the same denumerable set of variables,...
In this article, we characterize in terms of analytic tableaux the repairs of inconsistent relational databases, that is databases that do not satisfy a given set of integrity constraints. For this purpose we provide closing and opening criteria for branches in tableaux that are built for database instances and their integrity constraints. We use the tableaux based characterization as a basis for...
Controlled query evaluation enforces security policies for confidentiality in information systems. It deals with users who may apply background knowledge to infer additional information from the answers to their queries. For each query the correct answer is first judged by some censor and then - if necessary - appropriately modified to preserve security. In previous approaches, modification has been...
When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. In this paper, we use one of the paraconsistent logics introduced in [9,7] (LFI1) as a logical framework to model possibly inconsistent database instances obtained by integrating different sources.We propose a method based on the sound and complete tableau proof system of LFI1...
A relational database D is given with Ω as the set of attributes. The rows (tuples, data of one individual) are transmitted through a noisy channel. It is supposed that at most one data in a row can be changed by the transmission. We say that A → b (A ⊂ Ω, b ∈ Ω) is an error-correcting functional dependency if the data in A uniquely determine the data in b in spite of the error. We investigate the...
In this paper we show that the context model proposed by Gebhardt and Kruse (1993) can be semantically extended and considered as a data model for constructing membership functions of fuzzy concepts within the framework of meta-theory developed by Resconi et al. in 1990s. Within this framework, we integrate context models by using a model of modal logic, and develop a method for calculating the expressions...
Although the crucial role of if-then-conditionals for the dynamics of knowledge has been known for several decades, they do not seem to fit well in the framework of classical belief revision theory. In particular, the propositional paradigm of minimal change guiding the AGM-postulates of belief revision proved to be inadequate for preserving conditional beliefs under revision. In this paper, we present...
We address the problem of answering queries using expressive symmetric inter-schema constraints which allow to establish mappings between several heterogeneous information systems. This problem is of high relevance to data integration, as symmetric constraints are essential for dealing with true concept mismatch and are generalizations of the kinds of mappings supported by both local-as-view and global-as-view...
Microaggregation is a statistical disclosure control technique for protecting microdata (i.e., individual records), which are important products of statistical offices. The basic idea of microaggregation is to cluster individual records in microdata into a number of mutually exclusive groups prior to publication, and then publish the average over each group instead of individual records. Previous...
The idea to enforce consistency in databases tries to overcome widely known weaknesses for consistency checking and verification techniques. In general terms, a database transition S is systematically modified to a new transition SI (greatest consistent specialization, GCS) that is provably consistent with respect to a given static constraint I, preserves the effects...
This paper presents the Feature Decomposition Approach for improving supervised learning tasks. While in Feature Selection the aim is to identify a representative set of features from which to construct a classification model, in Feature Decomposition, the goal is to decompose the original set of features into several subsets. A classification model is built for each subset, and then all generated...
We say, that a database relation represents a Sperner system K on the set of attributes, if the system of minimal keys is exactly K. It is known, that such a representation always exsists. In this paper we show, that the maximum of the minimal number of tuples, that are needed to represent a Sperner system of only two element sets is 3(n/3+o(n)). We consider this problem for other classes of Sperner...
We define a new hierarchy in the class of computable queries to relational databases, in terms of the preservation of equality of theories in fragments of first order logic with bounded number of variables with the addition of counting quantifiers (Ck). We prove that the hierarchy is strict, and it turns out that it is orthogonal with the TIME-SPACE hierarchy defined with respect to Turing...
The problem of supporting updates to views of a database schema has been the focus of a substantial amount of research over the years. Since the mapping from base schema to view schema is seldom injective, there is usually a choice of possibilities for the reflection of view updates to base-schema updates. This work presents a solution to this problem which augments the constant-complement strategy...
The notion of an information system in Pawlak’s sense is extended by introducing a certain ordering on the attribute set, which allows to treat some attributes as parts of others. With every extended information system S associated is the set K(S) of those pieces of information that, in a sense, admit a direct access in S. The algebraic structure of the “information space” K(S) is investigated, and...
Cardinality constraints are a popular way of imposing restrictions to the structure of a database. In this paper, we consider global cardinality constraints which specify lower and upper bounds on the total number of relationships an entity of a fixed type may be involved in. It is natural to ask for the smallest database with non-empty domains that satisfies a given set of these constraints. For...
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