About the semantics of funtional dependencies

1999

Functional dependencies add semantics to a database schema, and are useful for studying various problems, such as database design, query optimization and how dependencies are carried into a view. In the context of a nested relational model, these dependencies can be extended by using path expressions instead of attribute names, resulting in a class of dependencies that we call nested functional dependencies (NFDs). NFDs dene a natural class of dependencies in complex data structures; in particular they allow the specication of many useful intra-and inter-set dependencies (i.e., dependencies that are local to a set and dependencies that require consistency between sets). Such constraints cannot be captured by existing notions of functional, multi-valued, or join dependencies. This paper presents the denition of NFDs and gives their meaning by translation to logic. It then presents a sound and complete set of eight inference rules for NFDs, and discusses approaches to handling the existence of empty sets in instances. Empty sets add complexity in reasoning since formulas such as 8x 2 R:P(x) are trivially true when R is empty. This axiomatization represents a rst step in reasoning about constraints on data warehouse applications, where both the source and target databases support complex types.

Encyclopedia of Database Systems, 2009

Functional dependencies are used in relational database design to show that the value of a set of attributes depends on the value of another set of attributes. Theory has been developed to manipulate a set of functional dependencies to describe equivalences of sets of functional dependencies. Semi-structured data differs from relational data in two important ways: semi-structured data is hierarchical and the structure of the data is less consistent. Traditional functional dependencies do not capture these differences so new functional dependencies with associated theory has been defined for semi-structured data.

IEEE Transactions on Knowledge and Data Engineering, 2016

Recently, there has been a renovated interest in functional dependencies due to the possibility of employing them in several advanced database operations, such as data cleaning, query relaxation, record matching, and so forth. In particular, the constraints defined for canonical functional dependencies have been relaxed to capture inconsistencies in real data, patterns of semantically related data, or semantic relationships in complex data types. In this paper, we have surveyed 35 of such functional dependencies, providing a classification criteria, motivating examples, and a systematic analysis of them.

HAL (Le Centre pour la Communication Scientifique Directe), 2015

This paper proposes "formalising functional dependencies" as an approach to address critical aspects of the potential of digital technologies for the teaching and learning of functions. This approach focuses on the role of the available tools in supporting students' transition from experiencing dependencies in terms of non-algebraic digital representations to expressing these dependencies formally. To illustrate the approach, data from two studies based on the use of two distinct computational systems are analysed. Key aspects of their potential include: work with dependencies at the level of magnitudes, specially designed functionalities and dynamic interplay between symbolic and non-symbolic representations of functions.

2001 ACM SIGPLAN, 2001

Functional dependencies help resolve many of the ambiguities that result from the use of multi-parameter type classes. They effectively enable writing programs at the type-level which significantly enhances the expressive power of Haskell's type system. Among the applications of this technique are the emulation of dependent types, and precise typechecking for XML and HTML combinator libraries. Unfortunately, the notation presently used for functional dependencies implies that the type-level programs are logic programs, but many of its applications are conceptually functional programs. We propose an alternative notation for functional dependencies which adds a functional-programming notation to Haskell's type classes and makes applications of functional dependencies significantly more readable. We apply the new notation to our examples and study the problems arising due to Haskell's open world assumption and overlapping instances.

Vietnam Journal of Computer Science

In general, there are two main approaches to handle the missing data values problem in SQL tables. One is to ignore or remove any record with some missing data values. The other approach is to fill or impute the missing data with new values [A. Farhangfar, L. A. Kurgan and W. Pedrycz, A novel framework for imputation of missing values in databases, IEEE Trans. Syst. Man Cybern. A, Syst. Hum. 37(5) (2007) 692–709]. In this paper, the second method is considered. Possible worlds, possible and certain keys, and weak and strong functional dependencies were introduced in Refs. 4 and 2 [H. Köhler, U. Leck, S. Link and X. Zhou, Possible and certain keys for SQL, VLDB J. 25(4) (2016) 571–596; M. Levene and G. Loizou, Axiomatisation of functional dependencies in incomplete relations, Theor. Comput. Sci. 206(1) (1998) 283–300]. We introduced the intermediate concept of strongly possible worlds in a preceding paper, which are obtained by filling missing data values with values already existing...

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.

2008

The paper proposes an extension of CFDs [1], referred to as extended Conditional Functional Dependencies (eCFDs). In contrast to CFDs, eCFDs specify patterns of semantically related values in terms of disjunction and inequality, and are capable of catching inconsistencies that arise in practice but cannot be detected by CFDs. The increase in expressive power does not incur extra complexity: we show that the satisfiability and implication analyses of eCFDs remain NPcomplete and coNP -complete, respectively, the same as their CFDs counterparts. In light of the intractability, we present an algorithm that approximates the maximum number of eCFDs that are satisfiable. In addition, we revise SQL techniques for detecting CFD violations, and show that violations of multiple eCFDs can be captured via a single pair of SQL queries. We also introduce an incremental SQL technique for detecting eCFD violations in response to database updates. We experimentally verify the effectiveness and efficiency of our SQL -based detection methods.

2012

Abstract. The treatment of many-valued data with FCA has been achieved by means of scaling. This method has some drawbacks, since the size of the resulting formal contexts depends usually on the number of different values that are present in a table, which can be very large. Pattern structures have been proved to deal with many-valued data, offering a viable and sound alternative to scaling in order to represent and analyze sets of many-valued data with FCA.

2000

The paper proposes an extension of CFD (1), referred to as extended Conditional Functional Dependencies (eCFD). In contrast to CFDs, eCFDs specify patterns of semanti- cally related values in terms of disjunction and inequality, and are capable of catching inconsistencies that arise in practice but cannot be detected by CFDs. The increase in expressive power does not incur extra complexity: