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[ontolog-forum] On Ontologies, Times, and Persons (was second attempt...

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Sun, 17 May 2015 13:52:02 -0400
Message-id: <5558D542.6070106@xxxxxxxxxxx>
Tom and Joe,    (01)

I changed the subject line to the title of Tom's .doc file (which I
copied below as plain text).    (02)

Tom
> Is anyone doing any work on this topic?    (03)

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    (04)

Joe
> We are expanding the work of John N. Warfield and others to include
> some of the features    (05)

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    (06)

Tom
> a distinction common in logic, the distinction between statements
> and propositions. A proposition is the semantic content of a set
> of synonymous statements.    (07)

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    (08)

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.    (09)

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.    (010)

In principle, that "solves" the problem.  But in practice, that
is just the beginning of a very hard problem.    (011)

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.    (012)

John
_______________________________________________________________________    (013)

On Ontologies, Times and Persons    (014)

by Tom Johnston, May 17, 2015    (015)

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.    (016)

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.    (017)

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.    (018)

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.    (019)

Is anyone doing any work on this topic?    (020)

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.    (021)

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).    (022)

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.    (023)

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.    (024)

It seems to me that this, too, is something worth keeping track of.
Is anyone doing work on this topic?    (025)

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?    (026)

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.    (027)

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.    (028)

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?    (029)

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.    (030)

(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.)    (031)

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.    (032)

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.    (033)

(If we represent specific propositional attitudes as a dimension, then 
we have a three-dimensional space.)    (034)

Once more, is anyone working on this topic?    (035)

Regards to all.
Tom Johnston    (036)

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