# Re: On Formal IS-A definition

From: Erwin <e.smout_at_myonline.be>

Date: Thu, 6 May 2010 02:47:59 -0700 (PDT)

Message-ID: <9fc21a72-6865-4a73-9183-a897275b6fdf_at_37g2000yqm.googlegroups.com>

On 6 mei, 09:00, "Mr. Scott" <do_not_re..._at_noone.com> wrote:

Date: Thu, 6 May 2010 02:47:59 -0700 (PDT)

Message-ID: <9fc21a72-6865-4a73-9183-a897275b6fdf_at_37g2000yqm.googlegroups.com>

On 6 mei, 09:00, "Mr. Scott" <do_not_re..._at_noone.com> wrote:

*> "Tegiri Nenashi" <tegirinena..._at_gmail.com> wrote in message**>**> news:0b2f71d0-34b5-4661-a8f6-21a40cdb9989_at_n37g2000prc.googlegroups.com...**>**>**>**>**>**> > Given the two relations R and S, the R is a subtype of S or simply "R**> > is an S" (was this the source of Reinier blunder?-) iff the two**> > conditions hold:**>**> > 1. R ^ S = R (where the ^ is natural join operation). This can be**> > expressed succinctly as R < S with generalized subset constraint "<".**>**> > The immediate consequence is that the attributes of S are the subset**> > of attributes R (formally: R ^ [] < S ^ [] where the "[]" is the**> > relation with empty set of attributes and empty set of tuples, aka**> > DUM). Then, one may add second requirement that**>**> > 2. Attributes of S form a key in relation R.**>**> > My question is if the condition #2 is really necessary. Consider the**> > two relations:**>**> > Animals = [Name]**> > bear**> > sheep**> > wolf**> > ;**>**> > Carnivores1 = [Name FavoritePrey]**> > bear deer**> > wolf sheep**> > ;**>**> > They satisfy both conditions so that informally we say "Carnivores1"**> > IS-A "Animals".**>**> > Contrast this with**>**> > Animals = [Name]**> > bear**> > sheep**> > wolf**> > ;**>**> > Carnivores2 = [Name Prey]**> > bear deer**> > wolf sheep**> > wolf deer**> > ;**>**> > I suggest that we still have "Carnivores2" IS-A "Animals". Do you**> > agree?**>**> There is a problem here. Which scheme is better?**>**> Employees{taxid,name,startdate} KEY{taxid},**> ContractEmployees{taxid,name,startdate,enddate} KEY{taxid},**> ContractEmployees[taxid,name,startdate] is a subset of**> Employees[taxid,name,startdate]**>**> or**>**> Employees{taxid,name,startdate} KEY{taxid},**> ContractEmployees{taxid,enddate} KEY{taxid},**> ContractEmployees[taxid] is a subset of Employees[taxid]**>**> Clearly the second scheme is equivalent to the first with respect to**> information content, so if a ContractEmployee is an Employee in the first**> scheme, then it must also be in the second, but in the second scheme, the**> set of attributes for Employees is not a subset of the set of attributes for**> ContractEmployees. I think the effect of the foreign key constraint,**> namely, that the components of the referenced tuple are effectively**> 'included' with the referencing tuple, must be taken into account.- Tekst uit oorspronkelijk bericht niet weergeven -**>**> - Tekst uit oorspronkelijk bericht weergeven -*The first is a violation of BCNF.

Well. I suspect you knew that too, and were just trying to make a point wrt the original question. Which, I must admit, I don't understand very well where it is headed, or why it was asked in the first place.

"Has-a" and "Is-a" are relationship types. As such, they occur in contexts of informal modeling such as ER and UML class diagram drawing. Inclusion constraints occur only in contexts of _FORMAL_ modeling where one is _effectively specifying ALL the details of some database definition_. As opposed to the context of informal modeling, where it is the _deliberate intention_ to make abstraction of some of the details. Received on Thu May 06 2010 - 04:47:59 CDT