with David McGoveran

(Title inspired by Richard Feynman)

I recently posted the following Fundamental Truth of the Week on LinkedIn, together with links to more detailed discussions of 1NF and 5NF (see References):“As currently defined, relational algebra produces anomalies when applied to non-5NF relations. Since an algebra cannot have anomalies, they should have raised a red flag that RA was not defined quite right, especially defining "relation" as a 1NF table and claiming algebraic closure because 1NF was preserved. Being restricted to tabular representation as the "language" for relationships is like being restricted to arithmetic when doing higher mathematics like differential calculus -- you need more expressive power, not less! Defining RA operations in terms of table manipulations aided initial learning and implementations by making data management look simple and VISUAL. Unfortunately, it was never grasped how much was missing, let alone how much more "intelligent" the RA and the RDBMS needed to be made to fix the problems. And I can see that those oversights were, in part, probably due to having to spend so much time correcting the ignorance in the industry."--David McGoveran

“According to conventional understanding of the RDM (such as it is) [and I don't mean SQL], a relation is in at least first normal form (1NF) -- it has only attributes drawn from simple domains (i.e., no "nested relations") -- the formal way of saying that a relation represents at the logical level an entity group from the conceptual level that has only individual entities -- no groups thereof -- as members. 1NF is required for decidability of the data sublanguage.It triggered a discussion that raised some fundamental issues for which an online exchange is too limiting. This post offers further clarifications, including comments by David McGoveran, on whose interpretation of the RDM (LOGIC FOR SERIOUS DATABASE FOLKS, forthcoming) I rely on. The portions of my interlocutor in the discussion are in quotes.

However, correctness, namely (1) system-guaranteed logical validity (i.e., query results follow provably from the database) and (2) by-design semantic consistency (of query results with the conceptual model) requires that relations are in both 1NF and fifth normal form (5NF). Formally, the only dependencies that hold in a 5NF relation are functional dependencies of non-key attributes on the PK -- for each PK value there is exactly one value of every corresponding non-key attribute value. This is the formal way of saying that a relation represents facts about a group of entities of a single type.

Therefore we now contend that database relations are BY DEFINITION in both 1NF and 5NF, otherwise all bets are off.”