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John Sowa makes interesting points in a recent
reply on the CG list. One doesn't get beyond
ontologies, but using operators on the ontological
lattice, one can make them dynamic. Implementing
such in XPath/XQuery, seems straightforward.
"No word can have a precise meaning outside of
a specific domain. That is even true of the
terms in mathematics and logic.
> So are you saying that categories used in models
> are fixed? That their meaning does not change
> depending on the terms which are grouped under them?
Just look at advanced textbooks in math & logic.
Every such textbook starts with a few pages of
definitions of the basic terms -- because every
mathematician or logician tends to use a different
choice of terminology and slightly different axioms.
Then for the remainder of that book, those terms
have a fixed definition that does not change during
that text, no matter how many additional definitions
and theorems are added to the subject.
When you talk about "meaning", however, there
can be and usually is an evolution of what people
sometimes call "connotation" -- the full range
of associated ideas and applications. In the
course of a book, more examples and applications
of the basic terms accumulate, and the reader
gets a wider and wider view of the ideas.
This accumulation of associations, however,
does not change the original definitions,
which are just as true at the end of the book
as at the beginning.
> Maybe for a given run or a given application
> of a model, but making a theory for modeling
> out of fixed categories could make it too
> inflexible for a theory that's supposed to be
> context-aware. Criteria may be fixed, but terms
> themselves do evolve, and the terms which denote
> categories within a model are no exception.
I certainly agree. That is why I have always
advocated a potentially infinite lattice of
theories. The labels of the concept or relation
types may be reused in multiple branches of the
lattice, but in different branches, they can have
different definitions. In that sense, evolution
means jumping from one branch of the lattice to
> Try to look back over any theory and you'll see
> that as criteria are added or modified, the
> categories change (even if their labels stay the same).
Yes, but then you have a different theory. See the
attached diagram navigate.gif, which shows the four
theory-revision operators, which are used to navigate
the lattice of all possible theories:
1. Expansion moves down the lattice to add more axioms
to a theory. That move leaves every statement that
was true in the smaller theory just as true as it
was before. However, there are now more statements
that can be proved.
2. Contraction moves up the lattice by deleting axioms.
Some statements that were true in the larger theory,
are no longer true.
3. Revision is a two-step operation of contraction
followed by expansion (or alternatively of expansion
followed by contraction). It is a sideways move
that may change the definitions of some terms.
4. And analogy jumps from one theory to another theory,
which is isomorphic to the first, but which has a
different selection of labels for the terms.
For further discussion of theory revision, see Chapter 6
of my KR book. I also discuss the navigate.gif diagram
in Section 7 of the following paper:
Signs, Processes, and Language Games
Summary: Every theory in the lattice is fixed for
all time, and expansion moves that go down the lattice
lead to larger theories in which all the previous
statements remain true. However, what you call
"evolution" is what I call "theory revision",
which makes sideways moves across the lattice.
From: Simon St.Laurent [mailto:email@example.com]
firstname.lastname@example.org (Bob Foster) writes:
>[Much excellence about family relationships changing over time.]
>The point about relationships being neither homogeneous nor stable
>over time, in either number or type, nor universally applicable, has
>been well made by William Kent, e.g., in his classic "Limitations of
>Record-Based Information Models" ACM TODS paper. Many of Kent's
>examples are cases where relationships change to meet business needs,
>e.g., cars can be leased to departments as well as individual drivers,
>which are changes in business practice.
I also very strongly recommend Kent's book _Data and Reality_. His
keynote at Extreme Markup Languages was excellent, though really just a
taste of the work he does, and _Data and Reality_ is an excellent tour
through these kinds of problems.
There are folks who dismiss these kinds of questions as merely
philosophical, but Kent makes them extremely concrete. The book is
twenty plus years old, and still utterly relevant.