Re: SUO: Re: SUO Ballot with 2 Questions
> And a registry is nothing more nor less than a method of
> indexing the modules and adding metadata about who, what,
> when, where, and why any changes, updates, revisions, or
> modifications were made.
This is a technical comment, and perhaps not quite on topic. But I think it
is important, and it may be of interest to others who might want to bookmark
it for later.
The notion of a formal concept lattice lies in the background of the FOL
lattice of theories and the FOL library of modules. A FOL library of modules
is situated in the context of a FOL lattice of theories, and a FOL lattice
of theories is base upon and closely related to the truth concept lattice of
the FOL language being used.
As we know, the notion of a formal concept lattice comes from Formal Concept
Analysis (FCA). Now, one of the central techniques of FCA is called
*conceptual scaling*. For further information, see any of the following.
* Bernhard Ganter and Rudolf Wille: (1999). Formal Concept Analysis --
Mathematical Foundations.
http://www.springer.de/cgi-bin/search_book.pl?isbn=3-540-62771-5
* Bernhard Ganter and Rudolf Wille: (1989). Conceptual scaling, in F.
Roberts (Ed.) Applications of Combinatorics and Graph Theory in the
Biological and Social Sciences, Springer-Verlag.
* Christian Neuss and Robert Kent: (1995). Conceptual Analysis of Resource
Meta-information
http://www.igd.fhg.de/archive/1995_www95/papers/94/www3.html
* Gerd Stumme: (2003). Lectures on Formal Concept Analysis
http://www.aifb.uni-karlsruhe.de/WBS/gst/FBA03/3_conceptual_scaling_en.pdf
From top-down conceptual scaling allows us to divide any formal concept
lattice into pieces that can be reassembled to get the original formal
concept lattice. One simple method for doing this is to partition the
collection of formal attributes, and to define a piece as the formal concept
lattice restricted to a particular partition block. From bottom-up one
method for building a formal concept lattice uses a building blocks
approach, where the blocks are called conceptual scales. Typically there is
one conceptual scale for each dimension of data.
To the case in point, the overall structure of the truth concept lattice,
and by extension the lattice of theories, can be partitioned into conceptual
scales according to topic, and one particular conceptual scale could be the
"metadata about who, what, when, where, and why any changes, updates,
revisions, or modifications were made". This information about the lattice
of theories can be part of the lattice of theories pointing out,
highlighting, and directing attention to the other parts of the lattice.
Bottom line: we can, somewhat by self-reference, apply our technique (using
the lattice of theories) to the technique itself.
Robert E. Kent
rekent@ontologos.org