Logical Design of Relational Database Systems

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.

Journal of the ACM, 1983

A class of database schemes, called acychc, was recently introduced. It is shown that this class has a number of desirable properties. In particular, several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity. In addition, several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given, and a smaple algorithm for determining acychclty is presented. Also given are several eqmvalent characterizations of those sets M of multivalued dependencies such that M is the set of muRlvalued dependencies that are the consequences of a given join dependency. Several characterizations for a conflict-free (in the sense of Lien) set of muluvalued dependencies are provided.

ACM SIGMOD Record, 1983

We study how functional dependencies affect the cyclicity of a database scheme; in particular, when does a set of functional dependencies make a cyclic database scheme behave like an acyclic one.A database scheme is fd-acyclic if every pairwise-consistent database state that satisfies the fd's is join-consistent. We give a simple characterization of fd-acyclicity over a restricted class of database schemes. We then give a tableau-based characterization for the general case that leads to an algorithm for testing fd-acyclicity. This algorithm actually solves the more general problem of query equivalence under functional dependencies and typed inclusion dependencies.

Fundamenta Informaticae

Codd's relational model describes just one possible world. To better cope with incomplete information, extended database models allow several possible worlds. Vague tables are one such convenient extended model where attributes accept sets of possible values (e.g., the manager is either Jill or Bob). However, conceptual database design in such cases remains an open problem. In particular, there is no canonical definition of functional dependencies (FDs) over possible worlds (e.g., each employee has just one manager). We identify several desirable properties that the semantics of such FDs should meet including Armstrong's axioms, the independence from irrelevant attributes, seamless satisfaction and implied by strong satisfaction. We show that we can define FDs such that they have all our desirable properties over vague tables. However, we also show that no notion of FD can satisfy all our desirable properties over a more general model (disjunctive tables). Our work formalizes a trade-off between having a general model and having well-behaved FDs.

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}).

1983

A class of integrity constraints for the relational model of data, called implicational dependencies over relational expressions (or, simply, IDEXs), is defined. The interest on IDEXs is justified by briefly indicating several logical database design problems where they naturally occur. To reason about IDEXs, a refutation procedure, which is a direct adaptation of first-order analytic tableaux, is introduced. Finally, the refutation procedure is shown to be a decision procedure for a restricted class of IDEXs.

Teubner-Texte zur Mathematik, 1991

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}).

International journal of biomedical soft computing and human sciences, 2000

Uhiversio, oj"Sciences. Vietnam (reeetved1ONovembet'l999,revisedcu2dac'cepted25Mevtrli2cr")y Abstraet 71his paper extencls the concept of.fi.tnctional dependency in a database in which the presence of context nutl vatues is atlou'ed. ft is shown that the set qfArmstreng 's injLirence rutes forms a sound and complete axiom s.ystem.forlitnctionai dependencies vvith context nulls as wett, Some rutesfor the dota update procedures are also introdttced and examined to ensure that the database ttnder consideration stilt satiofies a given set oflfitnetional dependencies.

Discrete Applied Mathematics, 1989

We present a formalization of certain data structures involved in the design of database management systems starting from abstractizations of the notions of functional and muhivalued dependencies in relational database systems (referred to as FD and MVD systems, respectively). The advantage of this abstract approach is a clarification of the essential properties of these data structures. Also, by identifying other objects which fit into the abstract concept we manage to transfer a number of intractable problems originating in graph theory and combinatorial set theory to the reahn of relational databases.

Information Sciences, 1987

We introduce the notion of an FD system on a semilattice as a generalization of the concept of a closed set of functional dependencies, and we study lattice-theoretical properties of those objects. The notion of a table as an abstraction of relations of relational databases is also considered, and a generalization of relational algebra is presented; this offers a better perspective on the role played by Armstrong's relations. Finally, an application of this algebraic approach to dynamic databases is included.