“Reasonable people adapt themselves to the world.

[joseph simpson <jjs0sbw@xxxxxxxxx>]

John:

The web site at:

http://www.jnwarfield.com/

Has a book section, if click on the book, "The Mathematics of Structure," you are taken to a second page:

http://www.jnwarfield.com/book2.htm

On this page if you click on "Book Store," a red link at the bottom of the page, you are taken to the book store where you can order copies of some of John Warfield's books.

I believe that they are still available.

I suggest "A Science of Generic Design," if it is available.

Societal Systems: Planning, Policy and Complexity is available used at Amazon for $62.52.

See:

http://www.amazon.com/Societal-Systems-Planning-Complexity-Engineering/dp/0471015695

A Science of Generic Design is available at Amazon for $82.10

See:

http://www.amazon.com/Science-Generic-Design-Managing-Complexity/dp/0813822475

Warfield augmented Boolean algebra by adding two operators:

The 'greater than' operator: 1 > 0

The 'less than' operator: 0 < 1

We have expanded Warfield's work to include the following concepts:

From empirical data: (standard Boolean semantics)

  0 = known false

  1 = known true

We have added:

  0 = unknown

  1 = inferred true

We use different colored backgrounds to indicate the semantic differences.

In machine processing other metadata could be used to represent the semantic differences.

We will be delivering some papers on our work at the University of Washington Bothell Campus on Wednesday, June 17th.  Please see the draft event notice at:

http://systemsconcept.org/html/Content/smp_arc/docs/06_06_2015/SMCPN.pdf

Take care, be good to yourself and have fun,

Joe

On Sun, May 17, 2015 at 10:52 AM, John F Sowa <sowa@xxxxxxxxxxx> wrote:

Tom and Joe,

I changed the subject line to the title of Tom's .doc file (which I
copied below as plain text).

Tom
> Is anyone doing any work on this topic?

Brief answer:  Yes, many people in many scattered locations with
many similar, but independently developed methods.  Some of them are
included among the 100+ documents I cited in the web page on "Semantics
for Interoperable Systems":  http://www.jfsowa.com/ikl

Joe
> We are expanding the work of John N. Warfield and others to include
> some of the features

Do you have any articles or slides about that work?  Amazon has a book
by Warfield for $102.  But it seems to have a lot of overlap with the
following "Handbook of Interactive Management", which you can download
for free:
http://demosophia.com/wp-content/uploads/2012/09/Handbook-of-Interactive-Management.pdf

Tom
> a distinction common in logic, the distinction between statements
> and propositions. A proposition is the semantic content of a set
> of synonymous statements.

One of the articles cited on that page defines a proposition as
an equivalence class of sentences that are related by a "meaning
preserving translation" (MPT).  That definition was adopted for
the definition of 'proposition' in the IKL logic.  See
http://www.jfsowa.com/logic/proposit.htm

Tom
> I think it must be the case that different ontologies, as sets
> of different statements, can express the same ontology, as a
> set of propositions.

Yes.  Any ontology can be considered a single sentence, namely
the conjunction of all the sentences in it.  Therefore, two
ontologies can be considered "the same" iff there is an MPT
that groups them in the same equivalence class.

In principle, that "solves" the problem.  But in practice, that
is just the beginning of a very hard problem.

There is much more to be said on all these issues.  The documents
cited in IKL cover many of the issues, and I'm always happy to add
more.

John
_______________________________________________________________________

On Ontologies, Times and Persons

by Tom Johnston, May 17, 2015

As many of you know, I'm interested in managing temporal data in
commercial databases, and have recently developed an ontology which
I think is common to all such databases.

One of the topics I still have a lot of work to do on is that of the
temporalization, and other relativizations, of formal ontologies themselves.

At one level, a formal ontology is expressed in a set of data structures
and instances of those structures. Let's call this the "inscriptional
level". If a formal ontology, call it Ont-X, exists on one computer and
then is copied to another computer, there then exists a second
inscription of that ontology. A branching process can lead to a tree of
inscriptions of Ont-X.

And as in biological evolution, or in the copying of manuscripts, errors
can be introduced in the copying process. Sometimes it might be
important to track down a particular error, and so it would be useful to
keep track of the provenance of those inscriptions of Ont-X.

Is anyone doing any work on this topic?

But this is just the issue of the temporalization of inscriptions of the
same ontology. What about the evolution of that ontology itself -- that
ontology as the semantics common to all those inscriptions? I consider
this distinction to be precisely the distinction between a statement and
the possibly many inscriptions of that statement.

So, as a semantic object, Ont-X may evolve over time. At times t1 and
t2, the ontological commitments expressed in Ont-X may differ. (Let's
assume that Ont-X remained semantically stable between t1 and t2).

Call the two ontologies Ont-X1 and Ont-X2. So there is a semantic
provenance also, in this case that the same ontology was originally
Ont-X1, and later became Ont-X2.

Now note the apparent inconsistency (intentional). I referred in the
same sentence to "two ontologies" and to "the same ontology". The
inconsistency is a simple terminological matter, I think. Because X1 and
X2 express different ontological commitments, it seems most natural to
call them different ontologies. But because X2 was created from X1, by
making some changes to X1, it is also possible to think of an ontology
-- Ont-X -- as an enduring semantic object that has changed over time,
that X1 is an earlier state of X and X2 a later successor state.

It seems to me that this, too, is something worth keeping track of.
Is anyone doing work on this topic?

Now consider two ontologies -- Ont-X and Ont-Y. Suppose that by means of
some intuitively natural translations, we find that X and Y, at the same
point in time, express the same ontology. What, in this context, does
"same ontology" mean?

Again, I analyze this by means of a distinction common in logic, the
distinction between statements and propositions. A proposition is the
semantic content of a set of synonymous statements. We now have a
many-to-one relationship between inscriptions and statements, and next a
many-to-one relationship between statements and propositions.

This is a harder problem than the first one. But just as we know that
"John loves Mary" and "Mary is loved by John" are two statements that
express the same proposition, I think it must be the case that different
ontologies, as sets of different statements, can express the same
ontology, as a set of propositions.

Of course, this is indeed a very hard problem. And because of my lack of
familiarity with the work done by ontology engineers, I can ask a third
question: is anyone doing work on this topic?

Now a final question. Just as there is a distinction between a statement
and an assertion by one or more persons, at a time t, that the statement
is (or is not) true, and also between a proposition and an assertion by
one or more persons, at a time t, that the proposition is (or is not)
true, there must be a distinction between an ontology as a set of
statements, or even as a set of propositions, and an assertion by one or
more persons that the ontology does or does not express their own
ontological commitments.

(A redundancy here: to assert that a statement is true is to assert that
the proposition expressed by the statement is true. But no matter, I
think, for this discussion.)

And here the provenance to be tracked is an evolving set of ontological
commitments, by a specific person or group of persons, at a point in
time or over a period of time. As the _expression_ of a set of ontological
commitments, then, an ontology is in fact relativized to a time t and a
person p. And just as a "language" is derivative from its component
dialects, and a dialect from its component idiolects, and an idiolect as
something that varies, for the person whose idiolect it is, over time, a
formal ontology, as the _expression_ of a set of ontological commitments,
is too.

People can make assertions and later withdraw them. They can express
other propositional attitudes, as well, such as doubt, approbation or
disapprobation, and so forth. And since the same person can change
propositional attitude towards the same propositions, and since the same
proposition can be asserted by one person at time t and denied by
another person at time t, there is an at least two-dimensional space in
which formal ontologies, as expressions of ontological commitments, can
exist and move about.

(If we represent specific propositional attitudes as a dimension, then
we have a three-dimensional space.)

Once more, is anyone working on this topic?

Regards to all.
Tom Johnston

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--

Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw

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