Modelling Functional Dependencies in Databases using Mathematical Logic (original) (raw)

An Efficient Extension Of Conditional Functional Dependencies Using Nested Relational Database

International journal of engineering research and technology, 2013

This paper propose an efficient data cleaning by using extended Conditional Functional Dependencies (eCFD’s), which is an extension of Conditional Functional Dependencies(CFD’s). eCFD’s intend to solve the multi-valued inconsistencies to trounce drawbacks of CFD’s which use pattern tableau to hold individual tuples in a table for cleaning relational data by supporting only single valued attributes. SQL techniques are used to create patterns of semantically related values for detecting single tuple CFD violations. By introducing a query and an algorithm we provide better competence for eliminating data redundancy in multi-valued attributes using nested relational database. We experimentally analyze the efficiency and performance of these eCFD based techniques in improving data quality and displays the tentative results graphically.

Functional dependencies in relational databases: A lattice point of view

Discrete Applied Mathematics, 1992

An equivalence is shown between functional dependency statements of a relational database, where "+" has the meaning of "determines," and implicational statements of propositional logic, where ".$" has the meaning of "implies." Specifically, it is shown that a dependency statement is a consequence of a set of dependency statements iff the corresponding implicational statement is a consequence of the corresponding set of implicational statements. The database designer can take advantage of this equivalence to reduce problems of interest to him to simpler problems in propositional logic. A detailed algorithm is presented for such an application. Two proofs of the equivalence are presented: a "syntactic" proof and a "semantic" proof. The syntactic proof proceeds in several steps. It is shown that I ) Armstrong's Dependency Axioms are complete for dependency statements in the usual logical sense that they are strong enough to prove every consequence, and that 2) Armstrong's Axioms are also complete for implicational statements in propositional logic. The equivalence then follows from 1) and 2). The other proof proceeds by considering appropriate semantic interpretations for the propositional variables. The Delobel-Casey Relational Database Decomposition Theorems, which heretofore have seemed somewhat fortuitous, are immediate and natural corollaries of the equivalence. Furthermore, a counterexample is demonstrated, which shows that what seems to be a mild extension of the equivalence fails.

IJERT-An Efficient Extension Of Conditional Functional Dependencies Using Nested Relational Database

International Journal of Engineering Research and Technology (IJERT), 2013

https://www.ijert.org/an-efficient-extension-of-conditional-functional-dependencies-using-nested-relational-database https://www.ijert.org/research/an-efficient-extension-of-conditional-functional-dependencies-using-nested-relational-database-IJERTV2IS3650.pdf This paper propose an efficient data cleaning by using extended Conditional Functional Dependencies (eCFD's), which is an extension of Conditional Functional Dependencies(CFD's). eCFD's intend to solve the multi-valued inconsistencies to trounce drawbacks of CFD's which use pattern tableau to hold individual tuples in a table for cleaning relational data by supporting only single valued attributes. SQL techniques are used to create patterns of semantically related values for detecting single tuple CFD violations. By introducing a query and an algorithm we provide better competence for eliminating data redundancy in multi-valued attributes using nested relational database. We experimentally analyze the efficiency and performance of these eCFD based techniques in improving data quality and displays the tentative results graphically.

The theory of functional and subset dependencies over relational expressions

Information Processing Letters, 1983

A formal system for reasoning about functional dependencies (FDs) and subset dependencies (SDS) defined over relational expressions is described. An FD e: X +Y indicates that Y is functionally dependent on X in the relation denoted by expression e; an SD e c f indicates that the relation denoted by e is a subset of that denoted by f. The system is shown to be sound and complete by resorting to the analytic tableaux method. Applications of the system include the problem of determining if a constraint of a subschema is implied by the constraints of the base schema and the development of database design methodologies similar to normalization.

Dependencies in relational data structures

Acta Cybernetica

PREFACE "It will be seen that logic can be used as a programming language, as a query language, to perform deductive searches, to maintain the integrity of data bases, to provide a formalism for handling negative information, to generalize concepts in knowledge representation, and to represent and manipulate data structures. Thus, logic provides a powerful tool for databases that is accomplished by no other approach developed to data. It provides a unifying mathematical theory for data bases." H. Gallaire, J. Minker April 1978 Today, database is a fascinating word. Commercial database management systems have been available for two decades, at the beginning in the form of hierarchical and network models. Two opposing research trends in database were created in the early -E (mployees) Address -Salary -D (epartments) Name -D (epartments) N (umbe) r -A (rticles) Name -M (arket) N (umbe) r (of the article) -M (arket) Price -Quantity -S (uppliers) Name -S (uppliers) Address -S (uppliers) N (umbe) r -S (uppliers) Price . The corresponding domains are obvious by the names and therefore omitted. Given now the following entity schemes Employees = ({EmpNr, EName, EAddress, Salary}, {EmpNr}), Department = ({DName, DNr}, {DNr}), Article = ({AName, MNr, MPrice, Quantity}, {MNr}), Supplier = ({SName, SAddress}, {SName, SAddress}).

An algebraic theory of functional and multivalued dependencies in relational databases

Theoretical Computer Science, 1987

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDS) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the 'generalized membership problem'.

Dependencies in Relational Databases

Teubner-Texte zur Mathematik, 1991

Normalization Based on Fuzzy Functional Dependency in a Fuzzy Relational Data Model

Information Systems, 1996

In many cases, classical databases need to be extended in order to represent and manipulate uncertain and imprecise information, In a fuzzy relational data model where attribute values are represented by possibility distributions and domains are associated with closeness relations, the problems of update anomalies and data redundancy may still exist. This paper aims to extend the normalization theory of the classical relational data model so as to provide theoretical guidelines for fuzzy relational database design. Based upon the notion of fuzzy functional dependency (FFD), a number of concepts such as relation keys and normal forms are generalized. As a result, q-keys, Fuzzy Fit Normal Form (FlNF), q-Fuzzy Second tiormal Form (q-F2NF). q-Fuzzy Third Normal Form (q-F3NF). and q-Fuzzy Boyce-Codd Normal Form (q-FBCNF) have been formulated. Finally, dependency-preserving and lossless-join decompositions into q-F3NFs are discussed.

An Equivalence Between Relational Database Dependencies and a Fragment of Propositional Logic

Journal of the Acm, 1981

It is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic Thins eqmvalence is extended to include both functional and multivalued dependencmes. Thus, for each dependency there is a corresponding statement m proposmonal logic. It ms then shown that a dependency (funcuonal or multivalued) is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement ~s a consequence of the corresponding set of proposmonal statements. Examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means It is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies.

Graphical axiomatization of sets of functional dependencies in relational databases

An important task during relational database schema design is to specify invariant properties, which the database instances must obey. These semantical conditions can be formulated as integrity constraints. The most fundamental type of constraints is functional dependency. Direct usage of its traditional formalism is rare in practice, due to its complexity and redundancies. However, in some cases, a complete and unambiguous specification can only be reached by using functional dependencies. We propose a novel approach for representing sets of functional constraints for small relational schemata. This graphical representation allows management of constraint sets much simpler and surveyable than the traditional notation. It supports reasoning on constraint sets in a natural way by an appropriate, powerful axiomatization and allows easy derivation. The axiomatization has an order of rule application property, yielding an algorithmic method for deriving the full knowledge an initial set...

Modelling Functional Dependencies in Databases using Mathematical Logic (original) (raw)

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