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## [ontolog-forum] puzzles

 To: patrick@xxxxxxxxxxx, "[ontolog-forum] " "Smith, Barry" Sun, 30 Apr 2006 18:15:30 +0200 <7.0.1.0.2.20060430174531.05867a20@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 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 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 {}, for which there are no subjects? Given what you say, we have for every positive integer n, proxies like: (}, }, and {, } as well as: {}, {}, {}, 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 {}? BS PS Is this an ISO Standard yet?
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