Reading
The listing below contains new books or articles that I have
found of interest as well as older gems that I have discovered while
researching a variety of subjects. Only brief comments are included
here, but occassionally I will post more extensive comments on a
particular work and those will be linked to from this listing.
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The Topos of Music: Geometric Logic of Concepts, Theory
and Performance, by Mazzola, Guerino. Birkäuser
Verlag, ISBN 3-7643-5731-2. Erratta Mazzola's homepage
This is an amazing work of European scholarship that
develops a formal mathematical concept of music. Along the way
it considers a wide range of topics, including category theory
as the basis for that theory. The work runs just over 1,300
pages, with a bibliography of 595 entries. A CD is included
with the volume that has the full text as a PDF file (and software), which
makes it possible take this work along while traveling.
I became interested in this work because category theory
looks like a useful tool for developing theories of subject
identity that can then be used in Topic Map Applications (not
software, the rules by which subjects are identified), also
referred to as TMA's.
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What is Knowledge Representation? by R. Davis,
H. Shrobe, P. Szolovits, AI Magazine, 14(1):17-33,
1993.
I actually found this resource while running the
citations in John Sowa's Knowledge
Representation. Compare this paper to Sowa's report of
it on page 134 of Knowledge Representation. I find
the original paper more persuasive than Sowa's
interpretation of it.
The fundamental issues in knowledge represenation have
not changed since this paper was published and have often
been discussed and debated with less insight that is found
within. Highly recommended.
The phrase, "running the citations" refers to the
practice of tracking the citations of an
author back to their sources and then the citations in
those sources back to their sources, etc. It is quite
instructive when, for example, a recent CS paper had one
citation to a non-existent article, fifteen citations that were
incorrect or incomplete, out of a total of twenty
citations.
At the very least ones gets an idea of how
carefully the author considered their sources, when citing
articles that simply don't exist or were not considered
important enough to merit correct citation. Such a
practice also aids in finding when a cited source does not
appear to support the proposition for which it is being
cited.
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HyTime ISO/IEC 10744:1992 (in pdf)
Actually I am re-reading the material on groves. Recall
that a grove (graph representation of property values) is
defined as: An abstract data structure consisting of a
directed graph of nodes in which each node may be connected
to other nodes by labeled arcs. (ISO/IEC 10744: 1992, 3.35)
That being the case, it appears that the notion of a node
having only one parent is an artifact of the SGML property
set. See directed
graph and simple
directed graph, both at MathWorld. Had a grove by its very nature
been restricted to a single parent for each node, the standard could
have easily defined a grove as simple directed graph.
I am interested in the notion of groves, separate and
apart from the architectural form trappings of ISO/IEC 10744
both as a means of handling overlapping hierarchies,
supporting interchange between divergent information systems and
as a mechanism for robust implementations of topic maps.
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