ADR's Normalization question

From: paul c <>
Date: Sat, 14 Nov 2009 00:00:41 GMT
Message-ID: <JqmLm.51902$Db2.37119_at_edtnps83>

In his 'Writings' series, this time from the 2006 edition, chapter 13,
'More on Normalization', Date examines a suggestion by one his
correspondents, known only as 'ADR'. This suggestion intrigued me, here's a longish quote for some context:

(start quote)
'... Note. Just to remind you, let me summarize those principles here:
1. A relvar that's not in fifth normal form (5NF) should be decomposed into a set of 5NF projections.
2. The original relvar should be reconstructable by joining those projections back together again.
3. The decomposition process should preserve dependencies. 4. Every projection should be needed in the reconstruction process.

'On the basis of this example I claimed that normalization by itself
wasn't enough: we needed something else to tell us what's wrong - what's formally wrong, I mean - with this decomposition. In fact, I claimed that what we needed was another principle (and later in the chapter I claimed that the principle in question was essentially The Principle of Orthogonal Design). ADR commented:

(ADR): "How about a principle stating that no attribute of the relvar being decomposed is to appear as a nonkey attribute in more than one projection? But I would not elevate such a simple and obvious rule to the status of a principle; I would just add it to the definition of the decomposition procedure. (That said, I admit that at the moment I'm still wondering if there are pathological cases that my suggested wording doesn't cater for.)"

(Date): 'There are several things I want to say ... (snip)
'But my major concern is that I think the proposed rule is too strong ...
'By way of example, suppose suppliers are partitioned into classes (C1,
C2, etc.), so that the supplier relvar has an additional attribute CLASS. Suppose also that (a) each class has just one associated status, and (b) each city has just one associated status as well, but (c) classes and cities are otherwise quite independent of each other. Then the relvar satisfies these two functional dependencies (FDs):

   { CLASS } -> { STATUS }
   { CITY } -> { STATUS } ...(snip)

'it should be apparent that the following is a valid nonloss
decomposition for this revised suppliers relvar (I ignore attribute SNAME for simplicity):

    SCC ( S#, CLASS, CITY}
        KEY { S# }     CLS { CLASS, STATUS}
        KEY { CLASS }     CTS { CITY, STATUS}
        KEY { CITY }
'Observe in particular that attribute STATUS appears here as a nonkey
attribute in more than one projection, and the decomposition thus violates ADR's proposed rule. Yet, to repeat, the decomposition is surely valid, and the proposed rule is thus not quite right.

(end quote)

I think that Date might be using a strawman argument here, ie., he shoots down an example which is a violation of ADR's suggestion.

If I'm not mistaken Armstrong's axioms can be applied to show that

   { CITY, CLASS } -> { STATUS }, so the CTS relation isn't needed if the CLS relation is replaced by

       KEY { CITY, CLASS } Have I got this right? If so, I think ADR's suggested rule does apply to Date's example. Received on Fri Nov 13 2009 - 18:00:41 CST

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