Data Dependencies in Codd's Relational Model with Similarities

Data Dependencies in Codd's Relational Model with Similarities

Radim Belohlavek (Binghamton University–SUNY, USA) and Vilem Vychodil (Palacky University, Czech Republic)
Copyright: © 2008 |Pages: 24
DOI: 10.4018/978-1-59904-853-6.ch025
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Abstract

This chapter deals with data dependencies in Codd’s relational model of data. In particular, we deal with fuzzy logic extensions of the relational model that consist of adding similarity relations to domains and consider functional dependencies in these extensions. We present a particular extension and functional dependencies in this extension that follow the principles of fuzzy logic in a narrow sense. We present selected features and results regarding this extension. Then, we use this extension as a reference model and compare it to several other extensions proposed in the literature. We argue that following the principles of fuzzy logic in a narrow sense, the same way we can follow the principles of classical logic in the case of the ordinary Codd relational model, helps achieve transparency, versatility, conceptual clarity, and theoretical and computational tractability of the extension. We outline several topics for future research.

Key Terms in this Chapter

Armstrong Rules: Armstrong rules are deduction rules for reasoning with functional dependencies. Usually, by Armstrong rules we mean a collection of rules that are syntactico-semantically complete. That is, a functional dependency semantically follows from a set T of functional dependencies iff can be obtained from T using Armstrong rules.

Functional dependency: Functional dependency is a formula where A and B are collections of attributes. being true in a table means that every two rows of a table that have the same values on attributes from A have the same values on attributes from B. Functional dependencies play important roles in the design of relational databases.

Structure of Truth Degrees: It is a set of truth degrees such as [0,1] equipped with truth functions of logical connectives. For instance, for the connective of implication, one can use (Lukasiewicz implication), or for and for a > b (Goguen implication). There are many choices of truth functions of logical connectives. However, the chosen collection of connectives should obey reasonable properties such as the adjointness property, which is required to be satisfied by the truth functions of conjunction and implication.

Codd’s Relational Model of Data: A theoretical model of data representation and manipulation by Edgar F. Codd (1960s, 1970s). Data are conceived as represented by tables in Codd’s model. A formal counterpart of a table is that of a relation. Data manipulation corresponds to performing operations with relations. Codd’s model relies on first-order logic and a mathematical concept of a relation. Codd’s relational model is the theoretical backbone of relational databases.

Domain with Similarity: A domain is a set of all possible values an attribute may take. For instance, a domain of the attribute age is a set {0,1,2,...,150}. A domain with similarity is a domain equipped with a particular binary fuzzy relation on it, called a similarity relation, that is, with a function assigning to every two elements of the domain a degree to which the two values are similar.

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Editorial Advisory Board
Program Committee
Table of Contents
Foreword
Maria Amparo Vila, Miguel Delgado
Preface
José Galindo
Acknowledgment
Chapter 1
José Galindo
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Introduction and Trends to Fuzzy Logic and Fuzzy Databases
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Chapter 2
Slawomir Zadrozny, Guy de Tré, Rita de Caluwe, Janusz Kacprzyk
In reality, a lot of information is available only in an imperfect form. This might be due to imprecision, vagueness, uncertainty, incompleteness... Sample PDF
An Overview of Fuzzy Approaches to Flexible Database Querying
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Chapter 3
Balazs Feil, Janos Abonyi
This chapter aims to give a comprehensive view about the links between fuzzy logic and data mining. It will be shown that knowledge extracted from... Sample PDF
Introduction to Fuzzy Data Mining Methods
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Chapter 4
Didier Dubois, Henri Prade
The chapter advocates the interest of distinguishing between negative and positive preferences in the processing of flexible queries. Negative... Sample PDF
Handling Bipolar Queries in Fuzzy Information Processing
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Chapter 5
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This chapter presents a discussion on fuzzy querying. It deals with the whole process of fuzzy querying, from the query formulation to its... Sample PDF
From User Requirements to Evaluation Strategies of Flexible Queries in Databases
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Chapter 6
P Bosc, A Hadjali, O Pivert
The idea of extending the usual Boolean queries with preferences has become a hot topic in the database community. One of the advantages of this... Sample PDF
On the Versatility of Fuzzy Sets for Modeling Flexible Queries
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Chapter 7
Guy De Tré, Marysa Demoor, Bert Callens, Lise Gosseye
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Flexible Querying Techniques Based on CBR
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Chapter 8
Bordogna Bordogna, Guiseppe Psaila
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Customizable Flexible Querying in Classical Relational Databases
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Chapter 9
Cornelia Tudorie
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Qualifying Objects in Classical Relational Database Querying
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Chapter 10
Ludovic Liétard, Daniel Rocacher
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Evaluation of Quantified Statements Using Gradual Numbers
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Chapter 11
Angélica Urrutia, Leonid Tineo, Claudia Gonzalez
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FSQL and SQLf: Towards a Standard in Fuzzy Databases
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Chapter 12
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Within the framework of flexible querying of possibilistic databases, based on the fuzzy set theory, this chapter focuses on the case where the... Sample PDF
Hierarchical Fuzzy Sets to Query Possibilistic Databases
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Chapter 13
Troels Andreasen, Henrik Bulskov
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Chapter 14
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Fuzzy relational databases have been introduced to deal with uncertain or incomplete information demonstrating the efficiency of processing fuzzy... Sample PDF
How to Achieve Fuzzy Relational Databases Managing Fuzzy Data and Metadata
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Chapter 15
Geraldo Xexéo, André Braga
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A Tool for Fuzzy Reasoning and Querying
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Chapter 16
Aleksandar Takaci, Srdan Škrbic
This chapter introduces a way to extend the relational model with mechanisms that can handle imprecise, uncertain, and inconsistent attribute values... Sample PDF
Data Model of FRDB with Different Data Types and PFSQL
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Chapter 17
Carlos D. Barranco, Jesús R. Campaña, Juan M. Medina
This chapter introduces a fuzzy object-relational database model including fuzzy extensions of the basic object-relational databases constructs, the... Sample PDF
Towards a Fuzzy Object-Relational Database Model
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Chapter 18
Radim Belohlavek
Formal concept analysis is a particular method of analysis of relational data. Also, formal concept analysis provides elaborate mathematical... Sample PDF
Relational Data,Formal Concept Analysis, and Graded Attributes
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Chapter 19
Markus Schneider
Spatial database systems and geographical information systems are currently only able to support geographical applications that deal with crisp... Sample PDF
Fuzzy Spatial Data Types for Spatial Uncertainty Management in Databases
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Chapter 20
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Chapter 21
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Chapter 22
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Chapter 23
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Chapter 24
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Incremental Discovery of Fuzzy Functional Dependencies
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Chapter 25
Radim Belohlavek, Vilem Vychodil
This chapter deals with data dependencies in Codd’s relational model of data. In particular, we deal with fuzzy logic extensions of the relational... Sample PDF
Data Dependencies in Codd's Relational Model with Similarities
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Chapter 26
Awadhesh Kumar Sharma, A. Goswami, D. K. Gupta
In this chapter, the concept of fuzzy inclusion dependencies (FIDas) in fuzzy databases is introduced and inference rules on such FIDas are derived.... Sample PDF
Fuzzy Inclusion Dependencies in Fuzzy Databases
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Chapter 27
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A Distributed Algorithm for Mining Fuzzy Association Rules in Traditional Databases
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Chapter 28
Yi Wang
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Applying Fuzzy Logic in Dynamic Causal Mining
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Chapter 29
Céline Fiot
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Fuzzy Sequential Patterns for Quantitative Data Mining
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Chapter 30
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Chapter 31
Malcolm Beynon
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Chapter 32
Malcolm Beynon
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Chapter 33
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Fuzzy Imputation Method for Database Systems
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Chapter 34
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