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[ontolog-forum] puzzles

To: patrick@xxxxxxxxxxx, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Smith, Barry" <phismith@xxxxxxxxxxx>
Date: Sun, 30 Apr 2006 18:15:30 +0200
Message-id: <>

I am trying, in my usual fumbling fashion, to understand your
13250-5 CD ( http://www.isotopicmaps.org/TMRM/TMRM-latest.html) document.

We have the following (all from pp. 1-2):

Subjects are represented by subject proxies (proxies ).

Proxies consist of properties ... which ? in turn ? may contain references to other proxies. This recursive relationship is defined via two postulated sets. One is the set of
labels , L . Each label from this set corresponds to exactly one proxy and vice-versa; ... The second set postulated here is V , a set of values. It contains values (such as numbers, strings, etc.), and all the labels in L .

property is the pair <h,k> in L x V. The set of all such properties is denoted as P .

EXAMPLE 1 Given the label
shoesize and the integer 43, then <shoesize , 43> is a property.

proxy is a finite set of properties, { p 1 , . . . , pn } , with p i in P.

The set of all proxies is the set of all subsets of
P : X = 2P

Subject proxies are composed of properties, each being a statement about the proxy?s subject.

This raises, e.g., the following questions:

each label from the set L corresponds to exactly one proxy and vice-versa, and if the set V contains L and all the numbers, then how is it possible that the set of proxies is of cardinality 2P ? Given that P itself is L x V, wouldn't this mean something like:

card(L) = card(2
LxAleph-0 )?

(Perhaps it is okay in topic maps to identify these two proxies.)

If subjects are 'represented by subject proxies (proxies )', then what about all those proxies, like

{<sleeps furiously, colorless green>},

for which there are no subjects?

Given what you say, we have for every positive integer n, proxies like:

(<prime, n>}, <not-prime, n>}, and {<prime, n>, <not-prime, n>}

as well as:

{<blue, n>}, {<creamy, n>}, {<not-identical-to-17, n>}, etc.

We are told that each property 'is a statement about the proxy's subject'.  Who makes all these statements? And what is the 'subject' of {<not-identical-to-17, 17>}?

PS Is this an ISO Standard yet?
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