Updated answer, Re: [sc34wg3] TMRM v6.0 comments

Thu, 28 Jul 2005 19:54:29 -0400

Nikita,

Well, I think we will get a definitive answer on Saturday morning when 
we cover the T+ model in some depth before turning to TMQL, but 
hopefully this will at least not be misleading:

Take a look at: http://en.wikipedia.org/wiki/Relational_algebra under 
the heading "The Cartesian product." I think this is what Robert is 
describing.

Hope you are having a great day!

Patrick

Nikita Ogievetsky wrote:

>Patrick,
>
>Thank you for trying to help. But...
>
>Per my understanding \what is attempted there is the following:
>(I replaced sigma with Sumx, etc. as I do not have Greek characters, and
>used "n" instead of "l")  
>
>Given two tuples:
>S1=Sum j(rj)=Sum j(<v1j,v2j...vnj>)
>S2=Sum i(ti)=Sum i(<x1i,x2i...xni>)
>r and t denote tuples, v and x denote values. 
>
>You arrive at:
>S1*S2 = Sum i(ti)* Sum j(rj) 
>= Sum i(ti) * Sum j(<v1j,v2j...vnj>)
>= Sum i(ti) * Sum j(<v1j><v2j...vnj>)
>= Sum i(ti) * Sum j(<v1j>)
>= Sum j,i(ti<vj>)
>
>1) How is it that 
>Sum j(<x1j,x2j...xnj>) = <x1j>*Sum j(<x2j...xnj>)?
>It is sum, not product, right?
>
>2) Why is <v2j...vnj> ignored?
>3) If it is ignorable, why don't you ignore <x2j...xnj> and arrive at even
>simple conclusion that:
>
>S1*S2 = Sum j,i(<xi><vj>)
>
>These do not make sense to me so far. Perhaps I do not understand
>notations...
>
>Have to run...
>
>Thanks,
>
>--Nikita
>
>PS:
>Sorry I will not be in Montreal... 
>Wish all to have a very productive meeting.
>
>
>! -----Original Message-----
>! From: sc34wg3-admin@isotopicmaps.org [mailto:sc34wg3-
>! admin@isotopicmaps.org] On Behalf Of Patrick Durusau
>! Sent: Wednesday, July 27, 2005 6:51 AM
>! To: sc34wg3@isotopicmaps.org
>! Subject: Re: Updated answer, Re: [sc34wg3] TMRM v6.0 comments
>! 
>! Nikita,
>! 
>! Nikita Ogievetsky wrote:
>! 
>! >Patrick,
>! >
>! >Thank you, - how did not I see "l" :-)
>! >
>! >
>! >
>! Err, because formal notation is more precise than English? ;-) Had I
>! tried to say the same thing in English, the error would have been obvious.
>! 
>! >However, I still have hard time with these formulas: (9) and (10).
>! >It is not clear what is the significance of the result, what did we try
>! to
>! >prove? It is also not clear how did we arrive from (9) to (10).
>! >In any case if it is correct, it means that the product between two tuple
>! >sequences (or ordered sets :-)) is not a symmetrical operation, which I
>! >really doubt. May be I am just missing something very obvious.
>! >I would greatly appreciate if you or Robert could help clarify this
>! >confusion.
>! >
>! >
>! >
>! I would have to ask Robert to be sure but it appears to me that there
>! are two separate tuple sequences, I assume a tuple sequence of keys and
>! a tuple sequence of values. Since all the operations described thus far
>! return tuples and sequences of tuples, the keys and values have to be
>! stitched back together.
>! 
>! Recall that earlier the statement is made: "All tuples in a tuple
>! sequence must have the same number of values."
>! 
>! That is only possible because the tuple sequence is the result of a
>! *path expression* being applied to a set of subject proxies.
>! 
>! In other words, just like an SQL expression, you are either going to get
>! a value or NULL for everything asked for in the expression. So, the all
>! the tuples in a tuple sequence will always have the same number of
>! values by definition.
>! 
>! Everything in section 4 depends upon that premise that we are working on
>! the result of a path expression.
>! 
>! Hope you are having a great day!
>! 
>! Patrick
>! 
>! PS: More replies after I get to Montreal later today. I have to finish
>! packing, etc.
>! 
>! 
>! >Thanks,
>! >
>! >--Nikita
>! >
>! >! -----Original Message-----
>! >! From: sc34wg3-admin@isotopicmaps.org [mailto:sc34wg3-
>! >! admin@isotopicmaps.org] On Behalf Of Patrick Durusau
>! >! Sent: Tuesday, July 26, 2005 10:23 AM
>! >! To: sc34wg3@isotopicmaps.org
>! >! Subject: Updated answer, Re: [sc34wg3] TMRM v6.0 comments
>! >!
>! >! Nikita,
>! >!
>! >! An updated answer to your third question:
>! >!
>! >! Nikita Ogievetsky wrote:
>! >!
>! >! > Dear Steve, Patrick, Robert, and all,
>! >! >
>! >! >
>! >! <snip>
>! >!
>! >! > 3) It is not clear what is in (.) between (v1j, v2j,.,v1j) in
>! >! > expression (9) on p11
>! >! >
>! >! Actually not a typo, just poor editorial practice.
>! >!
>! >! Using capital letters will make it plain:
>! >!
>! >! (v1j, v2j,...,vLj)
>! >!
>! >! The text uses a lower case "L" in the last term, which with a fairly
>! >! good magnifying glass is different from the number "1" in the subscript
>! >! for v at the beginning of the sequence.
>! >!
>! >! Same is true for the second sequence in that equation.
>! >!
>! >! That also happens in expression (12) on page 12, expressions (18),
>! (19),
>! >! and (20), on page 13, and expression (21) on page 14.
>! >!
>! >! Note that p_m is used in (13) on page 12, despite P_M being defined as
>! >! the set of all path expressions. In (13) it simply marks the last in a
>! >! sequence of path expressions.
>! >!
>! >! The usage of p_m is also inconsistent with p_n which you will find in
>! >! 4.2, condition #3.
>! >!
>! >! There are others I am sure I have not noticed yet so please feel free
>! to
>! >! point them out. Consistency and good editorial practice (like not using
>! >! graphically similar characters to mean different things) would go a
>! long
>! >! way to making the formalism easier to read.
>! >!
>! >! Sorry 'bout that!
>! >!
>! >! Hope you are having a great day!
>! >!
>! >! Patrick
>! >!
>! >! --
>! >! Patrick Durusau
>! >! Patrick@Durusau.net
>! >! Chair, V1 - Text Processing: Office and Publishing Systems Interface
>! >! Co-Editor, ISO 13250, Topic Maps -- Reference Model
>! >! Member, Text Encoding Initiative Board of Directors, 2003-2005
>! >!
>! >! Topic Maps: Human, not artificial, intelligence at work!
>! >!
>! >!
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>! >
>! >
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>! >
>! >
>! >
>! >
>! 
>! --
>! Patrick Durusau
>! Patrick@Durusau.net
>! Chair, V1 - Text Processing: Office and Publishing Systems Interface
>! Co-Editor, ISO 13250, Topic Maps -- Reference Model
>! Member, Text Encoding Initiative Board of Directors, 2003-2005
>! 
>! Topic Maps: Human, not artificial, intelligence at work!
>! 
>! 
>! _______________________________________________
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>! sc34wg3@isotopicmaps.org
>! http://www.isotopicmaps.org/mailman/listinfo/sc34wg3
>
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>
>  
>

-- 
Patrick Durusau
Patrick@Durusau.net
Chair, V1 - Text Processing: Office and Publishing Systems Interface
Co-Editor, ISO 13250, Topic Maps -- Reference Model
Member, Text Encoding Initiative Board of Directors, 2003-2005

Topic Maps: Human, not artificial, intelligence at work! 