[topicmapmail] context maps = application of set theory
W.M. Jaworski
wmj@gen-strategies.com
Wed, 2 May 2001 17:43:15 -0400
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[Martin Bryan]
Just been wondering whether set theory could be applied to topic maps. (Not
that I am a mathematician!). Here is a summary of my ramblings.
[wmj]
I am also not a mathematician. I only have a degree in mathematics from a
prestigious Mathematical Institute :-).
Here are MY (formal?) ramblings.
(1) I represented your original 8 tuples as a sequence - in case sequence is
important. (read vertically under S)
A {Context}
v original TM tuples
S {TM Tuple}
1 t1 pa1 n1 s1
2 t1 va1 o1 s1
3 t1 va2 o2 s2
4 t1 ua3 t2 s1
5 t2 pa1 n2 s1
6 t2 va1 o3 s1
7 t2 va2 o2 s2
8 t2 ua3 t1 s1
(2) I extracted "atoms" from your 8 tuples into the following sets:
{scope}
s1
s2
{topic}
t1
t2
{Varia}
pa1
va1
va2
ua3
{name}
n1
n2
{occurance}
o1
o2
o3
(3) I developed following Context (aka TM) schema/template (read vertically
like decision table)
A A {Context}
v original TM tuples
v context tuples
S {TM Tuple}
A {scope}
F {topic}
N {Varia}
N {name}
N {occurrence}
A, S, F, N are role types for relevant sets.
[For more sophisticated content/tuples the schema will be also more
sophisticated and build with more extensive list of set role types.]
(4) I recreated your 8 tuples in 8 columns by using "v" as role for set
members. (read vertically)
[For more "intelligent" tuples more extensive list of member's roles is
needed. ]
A A A A A A A A {Context}
v v v v v v v v context
tuples
A A A A A A A A {scope}
v v v v v v s1
v v s2
F F F F F F F F {topic}
v v v v v t1
v v v v v t2
N N N N N N N N {Varia}
v v pa1
v v va1
v v va2
v v ua3
N N N N N N N N {name}
v n1
v n2
N N N N N N N N {occurance}
v o1
v v o2
v o3
(5) Views from (1) and (4) are obtained by using queries against this
context map (shown at schema level):
I I 9 1 {cTuple Id}
A A 9 2 {Context}
v 1 original TM tuples
v 8 context tuples
S 1 8 {TM Tuple}
A 8 2 {scope}
F 8 2 {topic}
N 8 4 {Varia}
N 8 2 {name}
N 8 3 {occurance}
A A 9 1 {Content source}
v v 9 Content © by Martin Bryan
mtbryan@sgml.u-net.com
A A 9 1 {Author}
v v 9 Syntax and Patterns © by
wmj@gen-strategies.com , 1988-2001
I hope your e-mail (I am using MS Outlook) will display without distortions.
In a private mail I will send (to MB and SRN) views from (1) ... (5) in
color. (e-mail agent of topicmapmail intervenes when >40k)
If you are familiar with MS Excel I could send you the context map for
manipulation and expansion. You will need context map syntax but lets go
slowly but surely.
If you are still interested in my above "ramblings" than send me your
(reasonable size please) model in any representation together with extracted
set of sets (like in (2)). I will try to create Prototype Context of your
model (step (3), (4) and (5).) This will show cMap Syntax in action.
After that? Who knows?
Thanks for your insight and tuples.
WMJ
-----Original Message-----
From: topicmapmail-admin@infoloom.com
[mailto:topicmapmail-admin@infoloom.com]On Behalf Of Martin Bryan
Sent: Wednesday, May 02, 2001 3:23 AM
To: mb@infoloom.com; Steven R. Newcomb; topicmapmail@infoloom.com
Subject: [topicmapmail] Thinking aloud about the application of set
theory
Just been wondering whether set theory could be applied to topic maps. (Not
that I am a mathematician!). Here is a summary of my ramblings.
If we distinguish between predefined associations (pa) such as basename,
sortname, etc, and variable associations (va) such as those created by types
of occurrences, and user-defined associations (ua), such as those created by
association elements, then we end up with something like:
[t1 pa1 n1 s1
t1 va1 o1 s1
t1 va2 o2 s2
t1 ua3 t2 s1]
and
[t2 pa1 n2 s1
t2 va1 o3 s1
t2 va2 o2 s2
t2 ua3 t1 s1]
where t = topic, n=name, o=occurrence and s=scope. Can we then apply set
theory to query the set to create subsets that conform to particular scopes,
topics or associations?
Martin Bryan
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