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Re: [ontolog-forum] Sharing and Integrating Ontologies

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 07 Apr 2010 10:02:40 -0400
Message-id: <4BBC9080.40107@xxxxxxxxxxx>
The following note, which I sent to a discussion on an OMG list,
is related to PSL and other issues about the hierarchy of theories
in the SIO project.    (01)

John Sowa    (02)

-------- Original Message --------
Subject: Re: Business and logical view of processes
Date: Wed, 07 Apr 2010 09:30:51 -0400
From: John F. Sowa
To: architecture-ecosystem@xxxxxxx    (03)

Andre,    (04)

AC> Although PSL offers a very limited and narrow viewpoint to
 > knowledge architecture, it is interesting because it is quite
 > formal in its considerations.  It seems like a useful tool,
 > given the appropriate context and complementary environment.    (05)

The SIO project is designed to handle an open-ended number of
viewpoints on any imaginable topic.  The theoretical foundation
is based on an infinite lattice of all possible theories that
can be specified with a given logic.    (06)

Although infinity is beyond the scope of anything we can implement,
it ensures that any imaginable theory of any imaginable model has
a place somewhere within that infinity.  For the actual theories
that have been defined and tested, we have a more modest term:    (07)

    The hierarchy of certified theories    (08)

This hierarchy is a subset of the lattice that contains implemented
and tested theories (modules) from which larger ontologies can be
constructed.  It also contains combinations of modules that have
been assembled.  Since there is no upper limit on the size of
any module, they could include complete ontologies of any size.    (09)

Re PSL:  That is the Process Specification Language, which is one
useful theory that is contained in the COLORE collection (COmmon
Logic Ontology REpository), and COLORE is one of the starting
contributions to the SIO project.    (010)

However, there are other process theories that have been developed,
and they can also be included in the hierarchy.  For example,
Petri nets (another ISO standard) are widely use to define and
represent processes, and they are also the foundation for the
UML activity diagrams.    (011)

But the fact that the axioms that define Petri nets are different
from those that define PSL does not mean that they are incompatible.
In fact, the axioms for both viewpoints are consistent, and they
can be combined in a larger theory.  The combined theory has the
advantages of both:    (012)

  1. Any software based on PSL, Petri nets, or activity diagrams
     can be used to describe and process aspects of the combined
     theory or any ontology that includes it as one component.    (013)

  2. However, tools that were designed for just one of the viewpoints
     might not be able to represent and reason about all the details
     specified by the combined theory.  (That point is also true of
     the various UML diagrams, each of which can represent only one
     viewpoint on any particular system.)    (014)

  3. Another process theory is the pi-calculus, originally defined
     by Robin Milner.  Pi-calculus is an extension of Petri nets,
     and it is used in some methodologies, such as Business Process
     Modeling.  The axioms for pi-calculus are compatible with PSL,
     and a combined theory that includes both pi-calculus and PSL
     axioms could be defined and used.    (015)

  4. However, pi-calculus goes beyond Petri nets by allowing arcs
     of the nets to be created and destroyed dynamically.  Therefore,
     most tools designed just for Petri nets cannot handle pi-calculus
     applications with dynamically created arcs.  But pi-calculus
     tools could handle Petri net theories.    (016)

  5. But PSL is in the common intersection of all these theories,
     and any tools designed for PSL can be used to reason about
     anything in the common intersection.    (017)

This is an example of how the hierarchy can handle a multiplicity
of viewpoints, some of which are compatible with one another while
others may be inconsistent with one another.    (018)

For more about any of these systems, use your favorite search engine.
Following is an example of a proprietary system that uses pi-calculus:    (019)

http://www.fairdene.com/picalculus/workflow-is-just-a-pi-process.pdf    (020)

The important point I want to stress is that the hierarchy is neutral
with respect to any particular viewpoint, and it can be extended to
accommodate an open-ended number of viewpoints, many of which might
be inconsistent with one another.  Some further observations:    (021)

  1. The hierarchy can show explicitly which theories are consistent
     or inconsistent with other theories in the hierarchy.    (022)

  2. But it can't show the consistency or inconsistency until somebody
     has applied some tool to test that and has recorded the results
     of the test in the metadata associated with the hierarchy.    (023)

  3. Fortunately, the SIO project already has some tools for checking
     consistency or inconsistency and for using the results of previous
     tests to make inferences about combinations that don't need to
     be tested.    (024)

  4. Even more fortunately, the hierarchy supports methodologies for
     extending theories or combining theories in ways that preserve
     consistency.    (025)

John Sowa    (026)

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