# Codd's Relational Model from the Point of View of Fuzzy Logic

@article{Belohlvek2011CoddsRM, title={Codd's Relational Model from the Point of View of Fuzzy Logic}, author={Radim Belohl{\'a}vek and Vil{\'e}m Vychodil}, journal={J. Log. Comput.}, year={2011}, volume={21}, pages={851-862} }

The article deals with Codd's relational model of data and its fuzzy logic extensions. Our main purpose is to examine, from the point of view of fuzzy logic in the narrow sense, some of the extensions proposed in the literature and the relationships between them. We argue that fuzzy logic in the narrow sense is important for the fuzzy logic extensions because it provides conceptual and methodological foundations, clarity and simplicity. We present several comparative observations as well as new…

## Tables from this paper

## 19 Citations

Functional Dependencies Analyse in Fuzzy Relational Database Models

- Computer Science
- 2011

This paper presents a literature overview of Fuzzy Relational Database Models with emphasis on the role of functional dependencies in logical designing and modeling and considered the most important results.

Fuzzy Implication and Functional Dependency on Formal Context

- Computer Science
- 2020

This work shows difference and equivalence condition between fuzzy implication and fuzzy functional dependency and uses Armstrong’s rule to define soundness and completeness of the implication and fuzzy functional dependency model.

Attribute dependencies for data with grades I*,†

- Computer ScienceInt. J. Gen. Syst.
- 2016

It is argued that a reasonable theory of dependencies may be developed by making use of mathematical fuzzy logic, a recently developed many-valued logic, which is based on a solid logic calculus the same way classical dependencies are based on classical logic.

Parameterizing the Semantics of Fuzzy Attribute Implications by Systems of Isotone Galois Connections

- Computer ScienceIEEE Transactions on Fuzzy Systems
- 2016

This work formalizes the general parameterizations, proposes bivalent and graded notions of semantic entailment of fuzzy attribute implications, and shows their characterization in terms of least models and complete axiomatization.

Query systems in similarity-based databases: logical foundations, expressive power, and completeness

- Computer ScienceSAC '10
- 2010

The foundations for an extension of Codd's relational model of data are outlined and two query systems for similarity-based databases are proposed: a domain relational calculus (DRC) and a relational algebra (RA).

Logical Foundations for Similarity-Based Databases

- Computer ScienceDASFAA Workshops
- 2009

It is argued that similarity- based data manipulation can be made an integral part of an extended, similarity-based, relational model of data, rather than glued atop the classic relational model in an ad hoc manner.

Relational similarity-based model of data part 2: dependencies in data

- Computer ScienceInt. J. Gen. Syst.
- 2018

The paper shows that various aspects of dependencies in ranked data tables over domains with similarities can be properly formalized using complete residuated lattices as structures for similarities and ranks.

Derivation digraphs for dependencies in ordinal and similarity-based data

- Computer ScienceInf. Sci.
- 2014

## References

SHOWING 1-10 OF 52 REFERENCES

Fuzzy Relational Systems: Foundations and Principles

- Computer Science
- 2002

This text discusses phenomena hidden in the ordinary bivalent case, as well as new topics in fuzzy relational systems, such as object-attribute fuzzy relations and fuzzy concept latices, similarity, and fuzzy closure operators.

A new definition of fuzzy functional dependency in fuzzy relational databases

- Computer ScienceInt. J. Intell. Syst.
- 1994

A fuzzy extension of this concept to overcome the previous anomalous behaviors and study its properties is introduced, and the completeness of this fuzzy version of Armstrong axioms is of primary interest.

Mathematical Principles of Fuzzy Logic

- Computer Science
- 1999

Preface. 1. Fuzzy Logic: What, Why, for Which? 2. Algebraic Structures for Logical Calculi. 3. Logical Calculi and Model Theory. 4. Fuzzy Logic in Narrow Sense. 5. Functional Systems in Fuzzy Logic…

A complete axiomatization of fuzzy functional dependencies using fuzzy function

- Computer ScienceFuzzy Sets Syst.
- 2005

Fuzzy Functional Dependencies and Lossless Join Decomposition of Fuzzy Relational Database Systems

- Computer ScienceACM Trans. Database Syst.
- 1988

It is proved that with a suitable restriction on EQUAL, the design theory of a classical relational database with functional dependencies can be extended to fuzzy relations satisfying fuzzy functional dependencies.

Mining functional dependencies from fuzzy relational databases

- Computer ScienceSAC '00
- 2000

A level-wise mining technique is adopted here for the search of all possible nontrivial minimal functional dependencies defined by Bosc, and as the dependencies discovered are both representational and semantic, database schema design and query optimization can be directly benefited.

Fuzzy functional dependencies-an overview and a critical discussion

- Computer ScienceProceedings of 1994 IEEE 3rd International Fuzzy Systems Conference
- 1994

A critical overview of different proposals to deal with ill-known or weighted data in database management systems has been provided, and the intended semantics and use of fuzzy functional dependencies are particularly discussed.

Fuzzy Logic: Mathematical Tools for Approximate Reasoning

- Computer Science
- 2001

This logic is to investigate the wonderful human capacity of reasoning with vague notions by attempting to formalize the "approximate reasoning" the authors use in everyday life by proposing a general framework based on three mathematical tools: the theory of fuzzy closure operators, an extension principle for crisp logics and the Theory of recursively enumerable fuzzy subsets.

Fuzzy data dependencies and implication of fuzzy data dependencies

- Computer ScienceFuzzy Sets Syst.
- 1997

A computational algorithm for the FFD transitive closure and a complete axiomatization of fuzzy functional dependence (FFD)

- Computer ScienceInt. J. Intell. Syst.
- 1994

The FFD axiomatic system composed of four FFD inference rules is established and proven to be correct in terms of FFD logical implication with respect to the relation scheme, and the concept of the FFD transitive closure is defined, and correspondingly a computational algorithm is developed.