Re: Love or hate, or? domains with cardinality two

>> ... (*) It occurred to me that in Fagin's "A Normal Form for Relational
>> Databases That Is Based on Domains and Keys" he considers the
>> "combinatorial consequences of bounded domain sizes". It was something
>> about some logical equivalences not holding when domains of nonprime
>> attributes are "too small". But I don't recall all the details. Maybe,
>> rereading that paper will give me some insight.

> 
> I noticed nothing special there: in conclusion to that paper the author 
> stipulates that domain cardinality is greater or equal to 2.

Yes, a very weak condition. More interesting is the situation for prime attributes and join dependencies: there, cardinality constraints are less trivial:

• "too small" domains play a role on PJ/NF (Th. 6.10 of Fagin's paper);
• they cause an explosion in computational complexity at least for the problem of deriving join dependencies [1].

Nicola

[1] Kanellakis, 1980 (cited by Fagin)

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