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## Re: [ontolog-forum] Is there something I missed?

 To: "[ontolog-forum]" Ed Barkmeyer Fri, 30 Jan 2009 15:33:14 -0500 <4983640A.9070806@xxxxxxxx>
 ```Matthew West wrote: > Dear Mitch > >> - Any (relational) database schema describes a set of relations/an >> ontology and most are extremely multi-ary. > > [MW] Yes but these are mostly denormalisations to overcome the costs of > table joins.    (01) The whole aspect of arity of tables is bound up with the theory of "normal forms". Among other things, a table of 5 columns might still only represent a binary relation, and in "4th normal form" that is what it represents. The problem is how many columns it takes to provide the key values that identify each of the two participating individuals. So 4th normal form requires a table of n columns to express a function F of the form: F(c\1, ..., c\k) = (c\k+1, ..., c\n)    (02) So the table representing the total price of each line item of a purchase order may have four columns (order#, line#, amount, currency) where the function "total price" is: total_price (order#, line#) = (amount, currency) [4th NF] or (totalPrice lineItem monetaryAmount) [binary relation]    (03) It is only in "5th normal form" that all unary relations are one-column tables and all binary relations are two-column tables. And this is accomplished by creating artificial "identifiers" that correspond to "co-variant vectors" -- the "compound keys" for the individuals.    (04) The highly prized "3rd normal form" has the property Matthew observes: For each column c\i where i > k, c\i = F\i(c\1, ..., c\k) i.e., each data column is a function of _all_ the key columns, but there is no requirement for the data columns to have any other relationship to each other. All the functions are different. Thus the 3rd normal form table is the "natural join" of a set of "4th normal form" tables.    (05) Relational algebra is just yet another mathematical theory that has some relationships to knowledge engineering.    (06) -Ed    (07) -- Edward J. Barkmeyer Email: edbark@xxxxxxxx National Institute of Standards & Technology Manufacturing Systems Integration Division 100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528 Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694    (08) "The opinions expressed above do not reflect consensus of NIST, and have not been reviewed by any Government authority."    (09) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (010) ```
 Current Thread Re: [ontolog-forum] Is there something I missed?, (continued) Re: [ontolog-forum] Is there something I missed?, FERENC KOVACS Re: [ontolog-forum] Is there something I missed?, Pat Hayes Re: [ontolog-forum] Is there something I missed?, Mitch Harris Re: [ontolog-forum] Is there something I missed?, Matthew West Re: [ontolog-forum] Is there something I missed?, Mitch Harris Re: [ontolog-forum] Is there something I missed?, Patrick Cassidy Re: [ontolog-forum] Is there something I missed?, Schiffel, Jeffrey A Re: [ontolog-forum] Is there something I missed?, Mitch Harris Re: [ontolog-forum] Is there something I missed?, Ian Bailey Re: [ontolog-forum] Is there something I missed?, Matthew West Re: [ontolog-forum] Is there something I missed?, Ed Barkmeyer <= Re: [ontolog-forum] Is there something I missed?, Rich Cooper Re: [ontolog-forum] Is there something I missed?, Ed Barkmeyer Re: [ontolog-forum] Is there something I missed?, John F. Sowa Re: [ontolog-forum] Is there something I missed?, (•`'·.¸(`'·.¸(•)¸.·'´)¸.·'´•) .,., Re: [ontolog-forum] Is there something I missed?, John F. Sowa Re: [ontolog-forum] Is there something I missed?, Ian Bailey Re: [ontolog-forum] Is there something I missed?, Mike Bennett Re: [ontolog-forum] Is there something I missed?, Pat Hayes Re: [ontolog-forum] Is there something I missed?, Matthew West Re: [ontolog-forum] Is there something I missed?, Azamat