Path: news.f.de.plusline.net!news-fra1.dfn.de!kanaga.switch.ch!switch.ch!newsfeed-00.mathworks.com!NNTP.WPI.EDU!elk.ncren.net!newsflash.concordia.ca!News.Dal.Ca!ursa-nb00s0.nbnet.nb.ca!53ab2750!not-for-mail From: Bob Badour User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.2) Gecko/20040804 Netscape/7.2 (ax) X-Accept-Language: en-us, en MIME-Version: 1.0 Newsgroups: comp.databases.theory Subject: Re: Discovering new relationships References: <1172869458.132871.258340@h3g2000cwc.googlegroups.com> In-Reply-To: Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Lines: 76 Message-ID: Date: Sat, 03 Mar 2007 16:27:25 GMT NNTP-Posting-Host: 142.176.76.5 X-Complaints-To: abuse@aliant.net X-Trace: ursa-nb00s0.nbnet.nb.ca 1172939245 142.176.76.5 (Sat, 03 Mar 2007 12:27:25 AST) NNTP-Posting-Date: Sat, 03 Mar 2007 12:27:25 AST Organization: Business Internet Xref: news.f.de.plusline.net comp.databases.theory:42927 Walt wrote: > "Marshall" wrote in message > news:1172869458.132871.258340@h3g2000cwc.googlegroups.com... > >>On Mar 2, 12:01 pm, "Walt" wrote: > > >>>I think the two examples where I used SQL notation would be clearer if > > they > >>>were in mathematical notation, but I'm too timid to try. Can anybody > > help? > >>Ohhh! Ohhh! Pick me! >> >>----- >> >>& is used here for natural join. >> >>Consider your functions f and g. Let us imagine a "bind" operation, >>that gives names to both the parameter and return value of the >>procedural >>code f. Here is the syntax: >> >> y = f(x) >> >>So that expression (the whole thing: "y = f(x)") is interpreted as >> >> { (x, y) | y = f(x) } >> >>"The set of all x and y values where y is equal to f applied to x." >> >>Using this notation, let us rewrite your example. Assume j is a >>name that does not appear as an attribute of either R nor S. >> >> (R & (j = f(a))) & (S & (j = g(b))) >> >>This has a bunch of parens to avoid any ambiguities; we could >>also just write >> >> R & j=f(a) & S & j=g(b) >> >>Once you have bind and a complete set of relational operators, >>you can do anything SQL can do. (This also raises the question >>of what makes a good set of relational operators, which is an >>enormous topic on its own.) >> >>Darwen (and others) have an argument about the superiority of >>an algebraic relational language over one like SQL, which argument >>I find quite compelling. >> >> >>Marshall > > Thanks for the translation. Once I looked at it in mathematical notation, > it reminded me that a function is just a special case of a relation. From > there, I realized that I could have presented the example I gave without > having to use SQL "functions" at all. > > Let's say that we have two relations S(a) and R(b) with no "natural join" > between them. > All we need to do to relate the data is discover a relation T(a,b). Now > there's a natural join between S and T, and one between T and R. In the > abstract, such a relation always exists. > > The question, in data management terms is this: Is such a relation > "meaningful" in our universe of discourse? Stated in another way, is the > proposition that T represents one that says anything useful in the U of D? > This brings it back to data analysis. > > So I'm glad to have learned something, at the cost of having launched an > unnecessary discussion. I would rank it in the top three or four discussions in the past month.