Relationship between the Relational Database
                  Model and FCA

                                  Jaume Baixeries

                           Computer Science Department
                         Universitat Politcnica de Catalunya
                                Barcelona. Catalonia

    The Relational Database Model (RDBM) [3, 4] is one of the most relevant
database models that are being currently used to manage data. Although some
alternative models are also being used and implemented (namely, object oriented
databases and structured datatypes databases or NoSQL databases [1, 2]), the
RDBM still maintains its popularity, as some rankings indicate 1 .
    The RDBM can be formulated from a set-theoretical point of view, such that
a tuple is a partial function, and other basic operations in this model such as
projections, joins, selections, etc, can be seen as set operations.
    Another important feature of this model is the existence of constraints, which
are first-order predicates that must hold in a relational database. These con-
straints mostly describe conditions that must hold in order to keep the consis-
tency of the data in the database, but also help to describe some semantical
aspects of the dataset.
    In this talk, we consider some aspects of the RDBM that have been char-
acterized with FCA, focusing on different kinds of constraints that appear in
the Relational Model. We review some results that formalize different kinds of
contraints with FCA [5–8]. We also explain how some concepts of the RDBM
such as key, closure, completion, cover can be easily be understood with FCA.


References
1. Kai Orend. Analysis and Classification of NoSQL Databases and Evaluation of their
   Ability to Replace an Object-relational Persistence Layer. 2010. doi=10.1.1.184.483
2. A B M Moniruzzaman, Syed Akhter Hossain NoSQL Database: New Era of
   Databases for Big data Analytics. Classification, Characteristics and Comparison.
   arXiv:1307.0191 [cs.DB]
3. Codd, E. F. A Relational Model of Data for Large Shared Data Banks. Commun.
   ACM, 1970, volume 13, number 6.
4. Date, C. J. An Introduction to Database Systems (8 ed.). Pearson Education. ISBN
   0-321-19784-4.
5. Baixeries, Jaume. A Formal Context for Symmetric Dependencies. ICFCA 2008.
   LNAI 4933.
6. Baixeries, Jaume and Balcázar, José L. Characterization and Armstrong Relations
   for Degenerate Multivalued Dependencies Using Formal Concept Analysis. For-
   mal Concept Analysis, Third International Conference, ICFCA 2005, Lens, France,
   February 14-18, 2005, Proceedings. Lecture Notes in Computer Science, 2005
1
    http://db-engines.com/en/ranking
7. Baixeries, Jaume and Balcázar, José L. Unified Characterization of Symmetric De-
   pendencies with Lattices. Contributions to ICFCA 2006. 4th International Confer-
   ence on Formal Concept Analysis 2005.
8. Baixeries, Jaume. A Formal Concept Analysis framework to model functional de-
   pendencies. Mathematical Methods for Learning, 2004.