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Date: Fri, 27 Oct 1995 17:10:04 +0100
From: Catharina Kennedy <ck@ICS.inf.tu-dresden.de>
Subject: Re: Hierarchies, recursion...
To: Multiple recipients of list PRNCYB-L <PRNCYB-L@BINGVMB.BITNET>
Catharina Kennedy, ck@ics.inf.tu-dresden.de
I wish to reply to Cliff Joslyn:
> Yes, in a paper a few years back (see
> http://groucho.gsfc.nasa.gov/Code_520/Code_522/Tech_Collab/univ_contacts/
> joslyn/papers.html#JoC91c) I formally defined a hierarchy as any partially
> ordered structure.
I take it you mean the paper entitled "Hierarchy, Strict Hierarchy and
Generalised Information Theory" from 1991. That looks like it would
be very useful. Unfortunately I was only able to retrieve the first two
pages and I couldn't find out why. Is there an easier way of getting it
(the libraries here are very poor), or better still could you send me a
Postscript copy by Email?
>> R.Ramal, G.Toulouse and M.A.Virasoro (1986)
>> "Ultrametricity for Physicists", Review of Modern Physics 58,
>> pages 765-788.
>>
>> "Ultrametricity" is a property of hierarchies which is similar to the
>> law of transitivitiy in logic.
>
> Interesting. Is this a formal definition, or one tied to physical systems
> (being in a physics journal)?
Yes this is a formal definition, although for my work this paper has only
limited usefulness (since it is written for physicists, which I am not).
It is the only paper I know of where a formal definition of a hierarchy
is given, namely as a set H of subsets (of a universal set U) where each pair
of subsets must either be disjoint or an order must be enforced, i.e. one must
be a subset of the other. One thing I found interesting is that this
requirement reminds me of the conditions for information processing
(i.e the processes must either be seperate or an order must be enforced on
their interaction). Having said that, I think your definition would be better,
since it seems easier to visualise.
Over the issue of McCulloch and Heterarchy I will reply later, since this
is very complex.
regards,
Catharina
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Catharina Kennedy, ck@ics.inf.tu-dresden.de,
PhD student, Institute for Artificial Intelligence,
Faculty of Computer Science,
Technical University of Dresden,
01062 Dresden, Germany.
Tel: +49 351 4575 490
Fax: +49 351 4575 335
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