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In Part 1 we introduced in the conceptual model (CM) the metalogical designation property. It represents—in the absence of known shared defining properties of an entity type, the designation by a group's definer that an entity identifier (aka assigned name) or property value is a member of the group. Such a group is not a group of entities, but a group of name and property values. In the logical model (LM), it is formalized as a designation predicate (DP) and defines a domain.

In Part 2, we introduce the metalogical assertion property. It represents the assertion by an authorized database user that a specific entity, represented by a tuple, either does or does not correspond to an actual entity in the real world.

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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.

In response to a LinkedIn thread where interest was expressed in a "NULL research" project, we re-publish as "Oldies But Goodies" a series of old exchanges with readers reacting to our The Final NULL in the Coffin: A Relational Solution to Missing Data: in Parts 1, 2, 3  we re-published a past exchange between myself and Hugh Darwen with a reader on the pros and cons of our solution vs. Hugh Darwen's "horizontal decomposition" NULLless solution, and in Part 4 my debunking of reactions to an article of mine on the subject which exhibit the confusion inevitably evoked by NULL.

We complete this series with an exchange with a reader who claimed that our criticism applies to SQL's specific implementations of NULL, not to the NULL concept itself. I and David McGoveran explained that the implementation flaws in SQL derive directly from the deeper problems endemic to many-valued logics. 

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“What is the difference between an index and a key? How are they related?”

“There seams to be some confusion between what a Primary Key is, and what an Index is and how they are used. The Primary Key is a logical object. By that I mean that is simply defines a set of properties on one column or a set of columns to require that the columns which make up the primary key are unique and that none of them are null. Because they are unique and not null, these values (or value if your primary key is a single column) can then be used to identify a single row in the table every time. In most if not all database platforms the Primary Key will have an index created on it. An index on the other hand doesn’t define uniqueness. An index is used to more quickly find rows in the table based on the values which are part of the index. When you create an index within the database, you are creating a physical object which is being saved to disk.”

“A primary key by default creates a clustered index. A unique constraint/key by default creates a non-clustered index.”

“An index is a (logically) ordered list of rows. For example, an index on LastName means all values are already sorted in LastName order. Usually index rows contain far fewer columns in them than the table itself (except the clustered index, which is the table). A key is a column or columns that defines the order of an index. For example, on an index ordered by (LastName,FirstName), then LastName and FirstName are the keys. Btw, a primary key is a physical object, not a logical one. The db engine needs physical rows in order to insure unique values in the index.”

--Difference between an index and a key?, SQLTeam.com

I have recently published a paper[1], and posted a multipart series[2] on relational keys. In the latter I stated as follows:

"As a relational feature, keys can only be properly understood within the formal foundation of the RDM, which is simple set theory (SST) expressible in first order predicate logic (FOPL) adapted and applied to database management. Yet that is precisely what is ignored and dismissed in the industry -- including by the authors of SQL[3]."

I have also written extensively on widespread logical-physical confusion (LPC)[4], recently specifically in the key-index context[5]. The replies above are examples -- if any more were needed -- that validate my repeated claim of lack of foundation knowledge in the industry -- can you tell what's wrong with, and what's correct in, them?

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See: https://www.dbdebunk.com/2018/09/designation-property-and-assertion.html

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There is nothing wrong with Hugo Kornelis' picture of SQL NULL in NULL: The database's black hole. In fact, I recommend the series of which it is one part. It's SQL's picture of how to treat missing data that's wrong.

"Let’s first take a look at what NULL is supposed to be. Here is the definition of NULL from the SQL-2003 standard: null value--A special value that is used to indicate the absence of any data value."

While the absence of a value may be represented by some value at the implementation level, I strongly recommend users not think of NULL as any kind of value at the model level. The problems with NULL stem precisely from the fact that it is not a value, but rather a marker for the absence of a value. NULL value is a contradiction in terms that distracts from the problems.

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Conveying data fundamentals to practitioners, losing neither rigor, nor the audience is a difficult task. There are many experienced professionals with tool expertise, but poor foundation knowledge for which there is little regard. Even in academia education has been substituted by training, which is not the same thing.

One dilemma faced by an educator is the tension between the simplicity of examples effective for conveying general concepts or principles and the complexity of the reality to be represented in databases. The latter requires integration of many concepts and principles, as well as thorough business knowledge. This is part of the reason why I normally refrain from specific online modeling/design advice and limit myself to the general principles that must be adhered to in the process.

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Expertise in a field and ability to convey it to others are distinct and the latter requires different motivation, skills and talent. Many top technical experts are more often than not poor communicators, whether verbally or in writing, for some inherent reasons, Codd being an excellent example. That's one of the core reasons for poor foundation knowledge in data management in general, and the appreciation of the relational model in particular.

In a previous post I started a little experiment: I asked both readers who think they know and understand the relational model (RM) and those who do not but want to, to comment on whether a theoretically correct explanation of data fundamentals offered by reader PK was helpful and, if not, why not. I promised to draw some conclusions regarding the difficulty of dispelling misconceptions without losing either theoretical rigor, or the audience--a non-trivial task for an educator in an industry that deems theory impractical.

I can't say the response exactly answered my question (I recommend reading the comments, though). But let me, as promised, try my hand at making better sense of both the explanation and the comments (for an in-depth treatment see paper #1, Business Modeling for Database Design). Let me know if it helps..