“Fabian - With respect, maybe it's time to' shake the formal foundations' of data management, especially given the rising costs and increasing segregation of silos.”

“John, if I were to say what I really think, I would be accused of insulting, so I won't. You don't need to respect me, but you better respect formal foundations. Since they are what gives SOUNDNESS to data management practice, what you are really saying is that you don't care about soundness -- do you really intend to take this position? I would not be surprised, because the industry has long "shook" the formal foundations and lack of soundness is precisely what characterizes it. But because there is no longer proper education, practitioners are totally unaware of the relationship between formal foundations and soundness, everything is ad-hoc and arbitrary, yet they fail to recognize the consequences.”[1]Thus an exchange with John Gorman on LinkedIn, in which he posed several questions (that I answered in the last week's post[2]), the subject being the importance of not confusing levels of representation, and, more specifically, avoiding

--LinkedIn.com

**conceptual-logical conflation**(CLC)[3].

Somebody posted a link to my answers on Linkedin and in a comment on it John linked to a Richard Feynman YouTube lecture on "the general differences between the interests and customs of the mathematicians and the physicists". To which I responded that my very point is that, just like physics

*is not*the mathematics used to describe it (a central issue in quantum mechanics),

*conceptual modeling*, the latter is the representation of the former in the database -- they are distinct[2]. This brought to mind some older columns I published on the All Analytics website that no longer exists, so this series is a revision thereof.

__is not__data modeling------------------------------------------------------------------------------------------------------------------

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------------------------------------------------------------------------------------------------------------------

Mathematical relations are abstractions (i.e., devoid of any real world meaning), and, thus, can contain arbitrary data, and we can arbitrarily apply any operation of the relational algebra (RA) to them. For example, given the two relations A and B:100 26150 ...

110 38170 ...

120 37950 ...

130 33800 ...

140 35420 ...

150 30280 ...

160 27250 ...

290 15340 ...

310 15900 ...

... 100 06-19-1980 ...

... 110 05-16-1958 ...

... 120 12-05-1963 ...

... 130 07-28-1971 ...

... 140 12-15-1976 ...

... 150 02-12-1972 ...

... 160 10-11-1977 ...

... 290 05-30-1980 ...

... 310 09-12-1964 ...

*some subset *of Cartesian product of A with the projection of B on the second attribute --

all the possible combinations of each tuple of A with every tuple of the projection of B -- yields a relation, the attributes of which are those of A and the second attribute of B and the tuples of which are a subset of the tuples of the cross product. In mathematics the result is meaningless with respect to the real world.

But the RDM is *applied* relation theory: **simple set theory** (SST) expressible in **first order predicate logic** (FOPL) *adjusted for applicability to database management*. *Database* relations preserve mathematical properties, but -- distinct from mathematical relations -- are not abstract, but represent in the database sets of facts about real world entities identified during conceptual modeling:

- Tuples of base relations represent
**axioms**about entities (facts assumed to be true); - Tuples of RA derived relations represent
**theorems**(i.e., logical conclusions inferred from the axioms); - A DBMS and database constitute a
*logical inference*(i.e., deduction) engine that derives theorems from axioms.

*interpretations*(i.e., carry meaning specified by conceptual models that databases represent)[4,5]. Thus, conceptual and data modeling are distinct, which is why we advocate terminology that prevents confusion[6].

The data must be consistent with the conceptual model of reality intended by the modeler, which means that (1) neither the data in (2), nor the RA operations applicable to, database relations can be arbitrary -- both are

*constrained*by conceptual modeling and mathematics of the SST. If A and B were database relations representing facts about employee compensations and project assignments:

COMPENSATIONS {EMP#,SALARY,...}the result of the above Cartesian product (combining

ASSIGNMENTS {...,EMP#,START_DATE,...}

*each*salary with

*every*start date) wouldn't have a "sensible meaning", as a reader put it (i.e., the operation would not correspond to a meaningful query). As another commented, "Most of the real work in any query is planning out what you are asking, how you are asking it, and the meanings assigned." Which is another way of saying that users must understand the

*semantics*(meaning) of the data specified in the conceptual model by the modeler/database designer!, in order to query the database meaningfully (who must model in accordance to user perceptions of the world).

While it may be clear in this simple example that the operation makes no sense, this is often not the case in practice, as we shall demonstrate in Part 2.

**References**

[1] Software Wasteland How the Application-Centric Mindset is Hobbling our Enterprises.

[2] Pascal, F., Conceptual Modeling Is Not Data Modeling.

[3] Pascal, F., The Conceptual-Logical Conflation and the Logical-Physical Confusion.

[4] Pascal, F., What Relations Really Are and Why They Are Important.

[5] Pascal, F., What Meaning Means: Business Rules, Predicates, Integrity Constraints and Database Consistency.

[6] Pascal, F., Levels of Representation: Conceptual Modeling, Logical Design and Physical Implementation.

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