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Re: [ontolog-forum] Ontological Means for Systems Engineering

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 23 Jan 2009 09:38:21 -0500
Message-id: <4979D65D.2070201@xxxxxxxxxxx>
Dear Matthew and Ian,    (01)

Most of the practical applications of ontologies will be used for
things that could be called "systems".  But I agree with Matthew
that trying to distinguish artifacts from naturally occurring
things (i.e., created by physical processes and nonhuman organisms)
is not at all clear.  Furthermore, many systems (e.g., agricultural)
include living organisms.  And before businesses were computerized,
they had "Systems and Procedures" departments that specified a
"system" whose components were human beings -- including human
"computers".    (02)

MW> The two things that characterise a system for me are:
 >   1. It has a function/capability/purpose.
 >   2. Has parts that can be replaced by functionally equivalent parts.    (03)

I'm happy with that definition.  But I'd like to point out that
according to that definition, the human body is a system.    (04)

IB> To do this properly, and take into account trade-off, you need
 > to visit the murky worlds of Modal Logic and Possible Worlds
 > (David Lewis).  It's a pretty big piece of work to unpick a
 > fuzzy, imprecise subject like requirements and "ontologise" it.    (05)

I certainly agree with the last sentence, but I would add that
a great deal of the benefit can be derived just by having people
sit down, document it, analyze the interrelationships, and express
them clearly in ordinary language.  That kind of analysis is a
prerequisite to developing an ontology, and a very large part
of the benefit is derived from the analysis, long before anybody
converts the results to any kind of formal notation.    (06)

I would also like to point out that the "murky worlds of Modal Logic
and Possible Worlds" are not necessary for defining capabilities and
requirements.  The possible world models by Kripke were brilliant,
and they stimulated an enormous amount of murky ontology.  But the
logician Michael Dunn defined an equivalent semantics for modality
in terms of *laws and facts* without assuming any kind of possible
worlds -- or alternatively, by treating those "worlds" as colorful
metaphors for collections of statements that describe possibilities.    (07)

As an example of the use of Dunn's semantics, consider the popular
description logics.  Although those logics are first-order in their
expressive power, many DL proponents claim that they have a modal
effect.  That effect arises from the popular T-box and A-box:    (08)

  1. The T-box (Terminology definitions) are assumed to be fixed
     and have priority (greater "entrenchment") than mere
     assertions of fact.  In Dunn's sense, they are the *laws*
     for a family of descriptions of "possible worlds".    (09)

  2. The A-box (Assertion statements) use the terms defined in
     the T-Box to make statements of fact.  If any contradiction
     arises, the T-Box has priority, and the statements in the
     A-box must be revised.    (010)

In effect, the T-Box and the A-box are both collections of
first-order statements.  But outside those two boxes is a
metalevel statement about how they are related:    (011)

    If there is a contradiction between the T-box and any
    statement s in the A-box, the statement s is false.    (012)

This statement, which can also be stated in pure FOL, is a
metalevel statement, which makes an assertion about two
different collections of first-order statements.  In effect,
it declares the T-box statements to be "laws" with respect
to the ordinary "facts" in the A-Box.    (013)

The hierarchy of metalevels, each level purely first-order,
was defined by Tarski and developed by many other logicians,
including Dunn.  For a summary of that work and an application
of it for stripping the murky ontology from possible words,
see either or both of the following two papers:    (014)

    Laws, Facts, and Contexts: Foundations for Multimodal Reasoning    (015)

    Worlds, Models, and Descriptions    (016)

The second paper was written later, but it might be a better
place to start.  Read the first two sections of worlds.pdf
and then go to laws.htm.  The first four sections of laws.htm
cover Dunn's semantics, its relation to Kripke's possible
worlds, and Tarski's hierarchy of metalevels.    (017)

Later sections of those papers get into my own contributions,
but those aren't necessary to get the point about how the
hierarchy of metalevels and the distinction between laws and
facts can get rid of the mythology of possible worlds.    (018)

John Sowa    (019)

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