Revised 3/20/21

I recently came across a review of Edsger Dijkstra's work, where the following comment on a book he co-authored (referred to as D&S) raised my debunking antennae:

“... in general computer people seem to have a penchant for whipping up homebrew logics ... D&S is not the only example ... See E.F. Codd’s Relational Calculus, an obvious mess.”
--Maarten van Emden, A Bridge too Far: E.W. Dijkstra and Logic 

Having recently argued that "Codd was wrong" and "You're teaching [his] gospel" Betray Lack of Foundation Knowledge, my suspicion should hardly surprise. Besides, criticism of Dijkstra is a very tall order in itself, particularly in the context of disputes among logicians). As a reader asked, "What’s so obviously messy in Codd’s Relational Calculus?". Answer:

Note: Each "Test Your Foundation Knowledge" post presents one or more misconceptions about data fundamentals. To test your knowledge, first try to detect them, then proceed to read our debunking, reflecting the current understanding of the RDM, distinct from whatever has passed for it in the industry to date. If there isn't a match, you can review references -- reflecting the current understanding of the RDM, distinct from whatever has passed for it in the industry to date -- which explain and correct the misconceptions. You can acquire further knowledge by checking out our POSTS, BOOKS, PAPERS, LINKS (or, better, organize one of our on-site SEMINARS, which can be customized to specific needs).

“A relation, or table, in a relational database ... must have a set of columns or attributes, and it must have a set of rows to contain the data. A tuple (or row) can be a duplicate. In practice, a database might actually contain duplicate rows, but there should be practices in place to avoid this, such as the use of unique primary keys (next up). Given that a tuple cannot be a duplicate, it follows that a relation must contain at least one attribute (or column) that identifies each tuple (or row) uniquely. This is usually the primary key. This primary key cannot be duplicated.”

Misconceptions

• A relation is not a table and, thus, has neither fields, nor columns (which are not attributes) and rows;
• "Duplicate tuples" is a contradiction in terms -- a table with duplicate rows does not visualize a relation (i.e., is not a R-table) -- and a database with duplicated data is not relational;
• Without PKs a relation is not semantically consistent (i.e. it does not faithfully represent group of entities, which are distinguishable in the real world);

Fundamentals

• A database relation

- is a relationship among domains (sets of values) -- a subset of their cross-product -- a set of tuples (sets of values drawn from the domains) or, in other words, a set of sets from sets;
- has attributes, which are representations (1:1 mappings) of the domains in the relation;
- is semantically constrained to be consistent with (i.e., represent faithfully) the entity group in the conceptual model it represents in the database.

• A R-table visualizes a relation on some physical medium -- it plays no part in the relational model.

• Absence of PKs is semantic inconsistency with (inaccurate representation of) reality and a violation of the RDM.
  

Further Reading

What Relations Really Are and Why They Are Important

Understanding Relations series

What Is a Relational Database

Duplicates: Stating the Same Fact More Than Once Does Not Make it Truer, Only Redundant

Note: To demonstrate the correctness and stability due to a sound theoretical foundation relative to the industry's fad-driven "cookbook" practices, I am re-publishing as "Oldies But Goodies" material from the old DBDebunk.com (2000-06), Judge for yourself how well my arguments hold up and whether the industry has progressed beyond the misconceptions those arguments were intended to dispel. I may revise, break into parts, and/or add comments and/or references. You can acquire foundation knowledge by checking out our POSTS, BOOKS, PAPERS, LINKS (or, even better, organize one of our on-site SEMINARS, which can be customized to specific needs).

As part of the new understanding of the RDM we posted articles -- one last week -- about the types of properties and relationships at the conceptual level that are enforced via semantic constraints at the logical database level. One category of relationships exist among all members of an entity group, which are collective third order properties (3OP) of the group, enforced via multi-tuple constraints. There are at least two kinds of 3OP relationships: entity uniqueness, enforced via PK constraints and aggregate restriction, enforced via aggregation constraints. Practitioners are familiar with -- even if they do not necessarily have a full understanding of -- the former, but not so much with the latter. It so happens that they were the subject of an exchange between a reader of the old dbdebunk and C.J. Date. It is worth re-visiting as an example and, with the benefit of hindsight, to add some comments on re-publication.

Note: Each "Test Your Foundation Knowledge" post presents one or more misconceptions about data fundamentals. To test your knowledge, first try to detect them, then proceed to our debunking thereof. If there isn't a match, you can review references -- which reflect the current understanding of the RDM, distinct from whatever has passed for it in the industry to date -- which explain and correct the misconceptions. You can acquire further knowledge by checking out our POSTS, BOOKS, PAPERS and LINKS (or, better, organize one of our on-site SEMINARS, which can be customized to specific needs).

“[As a] set [a database relation] is a collection of similar or related things.”

--ArtfulSoftware.com

Can you tell what's wrong with this statement (hint: one word is wrong)? If not, it is because it is impossible without the old industry interpretation of the RDM.

Note: Each "Test Your Foundation Knowledge" post presents one or more misconceptions about data fundamentals. To test your knowledge, first try to detect them, then proceed to read our debunking, which is based on the current understanding of the RDM, distinct from whatever has passed for it in the industry to date. If there isn't a match, you can acquire the knowledge by checking out our POSTS, BOOKS, PAPERS, LINKS (or, better, organize one of our on-site SEMINARS, which can be customized to specific needs).

“The most popular data model in DBMS is the Relational Model. It is more scientific a model than others. This model is based on first-order predicate logic and defines a table as an n-ary relation. The main highlights of this model are:

• Data is stored in tables called relations.
• Relations can be normalized.
• In normalized relations, values saved are atomic values.
• Each row in a relation contains a unique value.
• Each column in a relation contains values from a same [sic] domain.”

--What is a relational database and why is it important, Quora.com

Note: To demonstrate the correctness and stability due to a sound theoretical foundation relative to the industry's fad-driven "cookbook" practices, I am re-publishing as "Oldies But Goodies" material from the old DBDebunk.com (2000-06), so that you can judge for yourself how well my arguments hold up and whether the industry has progressed beyond the misconceptions those arguments were intended to dispel. I may revise, break into parts, and/or add comments and/or references.

Skyscrapers with Shack Foundations

(originally posted 06/04/2000)

 “Well, it's really a judgment call and I think a lot of experience comes into it. It's a little bit like building a shack. Say you want to build a skyscraper, and you started out building a shack and you just keep trying to add onto it. After a while you have this severe structural problem ... So there is a fallacy to the build-upon-a-simple structure approach. Sometimes you get up to three stories and you have to do some major structural changes, and I just accept that.”
--Wayne Ratliffe, developer of dBase

“Client Servers were a tremendous mistake. And we are sorry that we sold it to you. Instead of applications running on the desktop and data sitting on the server, everything will be Internet based. The only things running on the desktop will be a browser and a word processor. What people want is simple, inexpensive hardware that functions as a window on to the Net. The PC was ludicrously complex with stacks of manuals, helplines and IT support needed to make it function. Client server was supposed to alleviate this problem, but it was a step in the wrong direction. We are paying through the nose to be ignorant.”
--Larry Ellison, CEO, Oracle Corp.

“To Normalize or not to Normalize? that really isn't a question. few things to consider:
Normalization is supposed to protect from data anomalies, but not prevent us from using data encapsulation is the magic trick that allows you to do what you want without breaking rules.what are your experiences with normalization?”

This is a question that at this time need -- and should -- not be asked anymore, and the fact that it still is is one confirmation -- among many -- that there is no progress in data management. According to the current understanding of the RDM:

• Database relations are both normalized (in 1NF) and fully normalized (in 5NF) by definition, otherwise they are not relations and the relational algebra (RA) does not work;
• Adherence to three database design principles produces 1NF and 5NF relational databases;
• Consequently, there should not be such a thing as "doing" normalization (to 1NF) and further normalization (to 5NF) except to repair databases that are non-relational due to failure to adhere to the principles.

Note: The three design principles are fundamental to SST/FOPL foundation of the RDM, but were never understood even by relational proponents. I do not know what encapsulation has to do with this.