Synthesizing third normal form relations from functional dependencies
ACM Transactions on Database Systems (TODS)
On the semantics of the relational data model
SIGMOD '75 Proceedings of the 1975 ACM SIGMOD international conference on Management of data
A unified approach to functional dependencies and relations
SIGMOD '75 Proceedings of the 1975 ACM SIGMOD international conference on Management of data
A complete axiomatization for functional and multivalued dependencies in database relations
SIGMOD '77 Proceedings of the 1977 ACM SIGMOD international conference on Management of data
Analysis and design of relational schemata for database systems.
Analysis and design of relational schemata for database systems.
A Proof Procedure for Data Dependencies
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Finitely Specifiable Implicational Dependency Families
Journal of the ACM (JACM)
Database design: composing fully normalized tables from a rigorous dependency diagram
Communications of the ACM
On the complexity of join dependencies
ACM Transactions on Database Systems (TODS)
Elimination of intersection anomalies from database schemes
Journal of the ACM (JACM)
A logical design methodology for relational databases using the extended entity-relationship model
ACM Computing Surveys (CSUR)
A new normal form for nested relations
ACM Transactions on Database Systems (TODS)
Unifying functional and multivalued dependencies for relational database design
PODS '86 Proceedings of the fifth ACM SIGACT-SIGMOD symposium on Principles of database systems
A formal view integration method
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Database theory—past and future
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Logical design of relational database schemes
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Computing covers for embedded functional dependencies
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A theory of intersection anomalies in relational database schemes
Journal of the ACM (JACM)
A synthesis algorithm for a class of 4NF
ACM SIGSMALL/PC Notes
The design of ¬ 1NF relational databases into nested normal form
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems
ACM Transactions on Database Systems (TODS)
Semantic database modeling: survey, applications, and research issues
ACM Computing Surveys (CSUR)
ACM Computing Surveys (CSUR)
Polynomial-time implication problems for unary inclusion dependencies
Journal of the ACM (JACM)
Independence-reducible database schemes
Journal of the ACM (JACM)
Simple conditions for guaranteeing higher normal forms in relational databases
ACM Transactions on Database Systems (TODS)
The practical need for fourth normal form
SIGCSE '92 Proceedings of the twenty-third SIGCSE technical symposium on Computer science education
Onion: a methodology for developing data-dominant systems from building blocks
TRI-Ada '94 Proceedings of the conference on TRI-Ada '94
Reduced MVDs and minimal covers
ACM Transactions on Database Systems (TODS)
An integrated approach to logical design of relational database schemes
ACM Transactions on Database Systems (TODS)
Deriving functional dependencies from the entity-relationship model
Communications of the ACM
A normal form for precisely characterizing redundancy in nested relations
ACM Transactions on Database Systems (TODS)
CSC '96 Proceedings of the 1996 ACM 24th annual conference on Computer science
Perspectives on database theory
ACM SIGACT News
How good is that data in the warehouse?
ACM SIGMIS Database
An Extended Relational Data Model For Probabilistic Reasoning
Journal of Intelligent Information Systems
SIGMOD '85 Proceedings of the 1985 ACM SIGMOD international conference on Management of data
On the design of relational database schemata
ACM Transactions on Database Systems (TODS)
Hierarchical schemata for relational databases
ACM Transactions on Database Systems (TODS)
An improved third normal form for relational databases
ACM Transactions on Database Systems (TODS)
A normal form for relational databases that is based on domains and keys
ACM Transactions on Database Systems (TODS)
Consequences of assuming a universal relation
ACM Transactions on Database Systems (TODS)
A formal approach to the definition and the design of conceptual schemata for databased systems
ACM Transactions on Database Systems (TODS)
On interpretations of relational languages and solutions to the implied constraint problem
ACM Transactions on Database Systems (TODS)
A simplied universal relation assumption and its properties
ACM Transactions on Database Systems (TODS)
Determining View dependencies using tableaux
ACM Transactions on Database Systems (TODS)
A new normal form for the design of relational database schemata
ACM Transactions on Database Systems (TODS)
Tree queries: a simple class of relational queries
ACM Transactions on Database Systems (TODS)
Computational problems related to the design of normal form relational schemas
ACM Transactions on Database Systems (TODS)
Limitations of record-based information models
ACM Transactions on Database Systems (TODS)
The theory of joins in relational databases
ACM Transactions on Database Systems (TODS)
Extending the database relational model to capture more meaning
ACM Transactions on Database Systems (TODS)
Efficient optimization of a class of relational expressions
ACM Transactions on Database Systems (TODS)
Testing implications of data dependencies
ACM Transactions on Database Systems (TODS)
Normalization and hierarchical dependencies in the relational data model
ACM Transactions on Database Systems (TODS)
On the menbership problem for functional and multivalued dependencies in relational databases
ACM Transactions on Database Systems (TODS)
Decompositions and functional dependencies in relations
ACM Transactions on Database Systems (TODS)
Workload models for DBMS performance evaluation
CSC '85 Proceedings of the 1985 ACM thirteenth annual conference on Computer Science
On Axiomatizing Multivalued Dependencies in Relational Databases
Journal of the ACM (JACM)
An Algorithm for Inferring Multivalued Dependencies with an Application to Propositional Logic
Journal of the ACM (JACM)
An Equivalence Between Relational Database Dependencies and a Fragment of Propositional Logic
Journal of the ACM (JACM)
On the Complexity of Testing Implications of Functional and Join Dependencies
Journal of the ACM (JACM)
An Almost Linear-Time Algorithm for Computing a Dependency Basis in a Relational Database
Journal of the ACM (JACM)
Subset Dependencies and a Completeness Result for a Subclass of Embedded Multivalued Dependencies
Journal of the ACM (JACM)
On the Equivalence of Database Models
Journal of the ACM (JACM)
A Complete Axiomatization of Full Join Dependencies
Journal of the ACM (JACM)
Testing satisfaction of functional dependencies
Journal of the ACM (JACM)
Properties of functional-dependency families
Journal of the ACM (JACM)
Horn clauses and database dependencies
Journal of the ACM (JACM)
On the family of generalized dependency constraints
Journal of the ACM (JACM)
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
On the Structure of Armstrong Relations for Functional Dependencies
Journal of the ACM (JACM)
The Logical Record Access Approach to Database Design
ACM Computing Surveys (CSUR)
Logic and Databases: A Deductive Approach
ACM Computing Surveys (CSUR)
A simple guide to five normal forms in relational database theory
Communications of the ACM
A history and evaluation of System R
Communications of the ACM
Communications of the ACM
The implication problem for inclusion dependencies: a graph approach
ACM SIGMOD Record
First order logic formalization for functional, multivalued and mutual dependencies
SIGMOD '78 Proceedings of the 1978 ACM SIGMOD international conference on management of data
A complete axiomatization for functional and multivalued dependencies in database relations
SIGMOD '77 Proceedings of the 1977 ACM SIGMOD international conference on Management of data
The Relational Structure of Belief Networks
Journal of Intelligent Information Systems
Synthesizing independent database schemas
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
Normal forms and relational database operators
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
Design of relational views over network schemas
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
Functional dependencies on cyclic database schemes
SIGMOD '83 Proceedings of the 1983 ACM SIGMOD international conference on Management of data
The interaction between functional dependencies and template dependencies
SIGMOD '80 Proceedings of the 1980 ACM SIGMOD international conference on Management of data
Inferences involving embedded multivalued dependencies and transitive dependencies
SIGMOD '80 Proceedings of the 1980 ACM SIGMOD international conference on Management of data
An entity-based database user interface
SIGMOD '80 Proceedings of the 1980 ACM SIGMOD international conference on Management of data
Can we use the universal instance assumption without using nulls?
SIGMOD '81 Proceedings of the 1981 ACM SIGMOD international conference on Management of data
A systematic approach to relational database theory
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
A technique for translating states between database schemata
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
Applying approximate order dependency to reduce indexing space
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
On the decomposition of join dependencies
PODS '84 Proceedings of the 3rd ACM SIGACT-SIGMOD symposium on Principles of database systems
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
Elimination of intersection amomalies from database schemes
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
Remarks on the algebra of non first normal form relations
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
Inclusion dependencies and their interaction with functional dependencies
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
A theory of data dependencies over relational expressions
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
An operational approach to data bases
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
The implication and finite implication problems for typed template dependencies
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
On Normalization of Relations in Relational Databases
Programming and Computing Software
Relational decomposition through partial functional dependencies
Data & Knowledge Engineering
Statistical Relational Databases: Normal Forms
IEEE Transactions on Knowledge and Data Engineering
Extending Existing Dependency Theory to Temporal Databases
IEEE Transactions on Knowledge and Data Engineering
Justification for Inclusion Dependency Normal Form
IEEE Transactions on Knowledge and Data Engineering
Constructing the Dependency Structure of a Multiagent Probabilistic Network
IEEE Transactions on Knowledge and Data Engineering
A Comparative Study of Various Nested Normal Forms
IEEE Transactions on Knowledge and Data Engineering
A Group-Select Operation for Relational Algebra and Implications for Database Machine Design
IEEE Transactions on Software Engineering
Fast In-Place Verification of Data Dependencies
IEEE Transactions on Knowledge and Data Engineering
Operations and the Properties on Non-First-Normal-Form Relational Databases
VLDB '83 Proceedings of the 9th International Conference on Very Large Data Bases
Comprehensive Approach to the Design of Relational Database Schemes
VLDB '84 Proceedings of the 10th International Conference on Very Large Data Bases
A Less Costly Constraints Checking for Join Dependency
VLDB '84 Proceedings of the 10th International Conference on Very Large Data Bases
Relational Databases for Querying XML Documents: Limitations and Opportunities
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
The Theory of Probabilistic Databases
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Efficiently Publishing Relational Data as XML Documents
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
An Abstract Introduction to the Temporal-Hierarchic Data Model (THM)
VLDB '83 Proceedings of the 9th International Conference on Very Large Data Bases
Database Decomposition into Fourth Normal Form
VLDB '83 Proceedings of the 9th International Conference on Very Large Data Bases
Equivalent Characterization of a Class of Conditional Probabilistic Independencies
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
About Tolerance and Similarity Relations in Information Systems
TSCTC '02 Proceedings of the Third International Conference on Rough Sets and Current Trends in Computing
About Conditional Belief Function Independence
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Efficiently publishing relational data as XML documents
The VLDB Journal — The International Journal on Very Large Data Bases
An information-theoretic approach to normal forms for relational and XML data
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Embedded implicational dependencies and their inference problem
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Properties of acyclic database schemes
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
A requirements and design aid for relational data bases
ICSE '81 Proceedings of the 5th international conference on Software engineering
Editing requirements for data base applications and their implementation on the INDY backend kernel
CAW '78 Proceedings of the fourth workshop on Computer architecture for non-numeric processing
Equivalence of relational database schemes
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A complete axiomatization for a large class of dependencies in relational datatbases
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Horn clauses and database dependencies (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Unary inclusion dependencies have polynomial time inference problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Decomposition of a relation scheme into Boyce-Codd Normal Form
ACM '80 Proceedings of the ACM 1980 annual conference
A semantic approach in designing relational data bases
ACM '78 Proceedings of the 1978 annual conference - Volume 2
Editing requirements for data base applications and their implementation on the INDY backend kernel
ACM SIGARCH Computer Architecture News
A note on decompositions of relational databases
ACM SIGMOD Record
A straightforward formalization of the relational model
ACM SIGMOD Record
Decomposition of a relation scheme into Boyce-Codd Normal Form
ACM SIGACT News
Supporting Semantic Diversity in the Relational Data Model: The Case of Multi-Face Attributes
Information Systems Frontiers
An approach to analyzing the information content of existing databases
ACM SIGMIS Database
Improving quality in conceptual modeling
OOPSLA '04 Companion to the 19th annual ACM SIGPLAN conference on Object-oriented programming systems, languages, and applications
Multi-valued dependencies in the presence of lists
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An information-theoretic approach to normal forms for relational and XML data
Journal of the ACM (JACM)
Functional and multivalued dependencies in nested databases generated by record and list constructor
Annals of Mathematics and Artificial Intelligence
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Axiomatisations of functional dependencies in the presence of records, lists, sets and multisets
Theoretical Computer Science - Logic, language, information and computation
On a problem of Fagin concerning multivalued dependencies in relational databases
Theoretical Computer Science
On the logical implication of multivalued dependencies with null values
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Efficient discovery of XML data redundancies
VLDB '06 Proceedings of the 32nd international conference on Very large data bases
Composition of mappings given by embedded dependencies
ACM Transactions on Database Systems (TODS)
Deciding implication for functional dependencies in complex-value databases
Theoretical Computer Science - Logic, language, information and computation
ACM SIGMOD Record
On inferences of full hierarchical dependencies
ACSC '07 Proceedings of the thirtieth Australasian conference on Computer science - Volume 62
Full hierarchical dependencies in fixed and undetermined universes
Annals of Mathematics and Artificial Intelligence
Design and performance tools for data base systems
VLDB '77 Proceedings of the third international conference on Very large data bases - Volume 3
A relational data language with simplified binary relation handling capability
VLDB '77 Proceedings of the third international conference on Very large data bases - Volume 3
The decomposition versus synthetic approach to relational database design
VLDB '77 Proceedings of the third international conference on Very large data bases - Volume 3
A consideration on normal form of not-necessarily-normalized relation in the relational data model
VLDB '77 Proceedings of the third international conference on Very large data bases - Volume 3
A sophisticate's introduction to database normalization theory
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
A normal form for abstract syntax
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
The information preserving properties of relational database transformations
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
Mutual dependencies and some results on undecomposable relations
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
On the updatability of relational views
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
Equivalence among relational expressions with the union and difference operation
VLDB '78 Proceedings of the fourth international conference on Very Large Data Bases - Volume 4
Towards a universal relation interface
VLDB '79 Proceedings of the fifth international conference on Very Large Data Bases - Volume 5
Multivalued dependencies with null values in relational data bases
VLDB '79 Proceedings of the fifth international conference on Very Large Data Bases - Volume 5
Algorithmic applications for a new result on multivalued dependencies
VLDB '79 Proceedings of the fifth international conference on Very Large Data Bases - Volume 5
Generalized mutual dependencies and the decomposition of database relations
VLDB '79 Proceedings of the fifth international conference on Very Large Data Bases - Volume 5
Database design tools: an expert system approach
VLDB '85 Proceedings of the 11th international conference on Very Large Data Bases - Volume 11
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
Impacts of logic and databases (invited paper)
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
VLDB '80 Proceedings of the sixth international conference on Very Large Data Bases - Volume 6
What does Boyce-Codd normal form do?
VLDB '80 Proceedings of the sixth international conference on Very Large Data Bases - Volume 6
Some analytic tools for the design of relational database systems
VLDB '80 Proceedings of the sixth international conference on Very Large Data Bases - Volume 6
ACM Transactions on Database Systems (TODS)
Maximal prime subgraph decomposition of Bayesian networks: A relational database perspective
International Journal of Approximate Reasoning
A Normalization Framework for Multimedia Databases
IEEE Transactions on Knowledge and Data Engineering
The implication problem for measure-based constraints
Information Systems
Constraint acquisition you can chase but you cannot find
APCCM '08 Proceedings of the fifth Asia-Pacific conference on Conceptual Modelling - Volume 79
Information Sciences: an International Journal
Functions of the database workbench
AFIPS '84 Proceedings of the July 9-12, 1984, national computer conference and exposition
A methodology for information system design
AFIPS '81 Proceedings of the May 4-7, 1981, national computer conference
Database-oriented decision support systems
AFIPS '83 Proceedings of the May 16-19, 1983, national computer conference
On Inferences ofWeak Multivalued Dependencies
Fundamenta Informaticae
Spoilt for Choice: Full First-Order Hierarchical Decompositions
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Constraint acquisition for Entity-Relationship models
Data & Knowledge Engineering
Functional dependencies in a relational database and propositional logic
IBM Journal of Research and Development
IBM Journal of Research and Development
The Implication Problem of Functional Dependencies in Complex-value Databases
Electronic Notes in Theoretical Computer Science (ENTCS)
An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Teaching a schema translator to produce O/R views
ER'07 Proceedings of the 26th international conference on Conceptual modeling
Appropriate reasoning about data dependencies in fixed and undetermined universes
FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
When data dependencies over SQL tables meet the logics of paradox and S-3
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Four lessons in versatility or how query languages adapt to the web
Semantic techniques for the web
The logic of representing dependencies by directed graphs
AAAI'87 Proceedings of the sixth National conference on Artificial intelligence - Volume 1
The logic of representing dependencies by directed graphs
AAAI'87 Proceedings of the sixth National conference on Artificial intelligence - Volume 1
On the role of the complementation rule for data dependencies over incomplete relations
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
CRIUS: user-friendly database design
Proceedings of the VLDB Endowment
On learning multivalued dependencies with queries
Theoretical Computer Science
Testing implication of probabilistic dependencies
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Generating graphoids from generalised conditional probability
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
Valuation networks and conditional independence
UAI'93 Proceedings of the Ninth international conference on Uncertainty in artificial intelligence
A graph-based inference method for conditional independence
UAI'91 Proceedings of the Seventh conference on Uncertainty in Artificial Intelligence
The nested list normal form for functional and multivalued dependencies
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
On multivalued dependencies in fixed and undetermined universes
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
Simplified integration of Prolog with RDBMS
ACM SIGMIS Database
The transformational approach to database engineering
GTTSE'05 Proceedings of the 2005 international conference on Generative and Transformational Techniques in Software Engineering
Characterisations of multivalued dependency implication over undetermined universes
Journal of Computer and System Sciences
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Foundations for a fourth normal form over SQL-Like databases
Conceptual Modelling and Its Theoretical Foundations
ACM Transactions on Database Systems (TODS)
Appropriate inferences of data dependencies in relational databases
Annals of Mathematics and Artificial Intelligence
A normal form for preventing redundant tuples in relational databases
Proceedings of the 15th International Conference on Database Theory
Negative results on learning multivalued dependencies with queries
Information Processing Letters
Generalized Quantifiers in Dependence Logic
Journal of Logic, Language and Information
On Inferences of Full First-Order Hierarchical Decompositions
Fundamenta Informaticae - Logic, Language, Information and Computation
On Inferences ofWeak Multivalued Dependencies
Fundamenta Informaticae
An efficient approach to identify n-wMVD for eliminating data redundancy
Proceedings of the CUBE International Information Technology Conference
XSym'07 Proceedings of the 5th international conference on Database and XML Technologies
Probabilistic conditional independence under schema certainty and uncertainty
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Exploiting data dependencies with null values for ontology extraction
ER'12 Proceedings of the 31st international conference on Conceptual Modeling
Atomicity and Semantic Normalization
International Journal of Information System Modeling and Design
Reasoning about functional and full hierarchical dependencies over partial relations
Information Sciences: an International Journal
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
APCCM '12 Proceedings of the Eighth Asia-Pacific Conference on Conceptual Modelling - Volume 130
On the logical implication of multivalued dependencies with null values
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
Relation decomposition: the theory
MLDM'13 Proceedings of the 9th international conference on Machine Learning and Data Mining in Pattern Recognition
An overview of recent data base research
ACM SIGMIS Database
Two Database Related Interpretations of Rough Approximations: Data Organization and Query Execution
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
| Hi-index | 0.08 |
A new type of dependency, which includes the well-known functional dependencies as a special case, is defined for relational databases. By using this concept, a new (“fourth”) normal form for relation schemata is defined. This fourth normal form is strictly stronger than Codd's “improved third normal form” (or “Boyce-Codd normal form”). It is shown that every relation schema can be decomposed into a family of relation schemata in fourth normal form without loss of information (that is, the original relation can be obtained from the new relations by taking joins).