[ontolog-forum] puzzles

["Smith, Barry" <phismith@xxxxxxxxxxx>]

Patrick,

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
> . 
>
> A 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.
>
> A 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:

If 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(2LxAleph-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>}? 

BS
PS Is this an ISO
Standard yet?