Speaking for myself, I don't think the library scientists will want to
master pi calculus either - RDF and OWL, axioms and inference I can
handle :-) (01)
Regards,
Antoinette (02)
Antoinette Arsic
Sr. Information Systems Engineer
The MITRE Corporation
703-337-9016 (VOIP)
*703-983-5286 (new office number, was 883)
*443-567-2703 (new cell) (03)
-----Original Message-----
From: ontac-forum-bounces@xxxxxxxxxxxxxx
[mailto:ontac-forum-bounces@xxxxxxxxxxxxxx] On Behalf Of John F. Sowa
Sent: Wednesday, January 11, 2006 1:50 AM
To: Michael Gruninger
Cc: 'SUO WG'; CG; ONTAC-WG General Discussion
Subject: Re: [ontac-forum] Re: The world may fundamentally be
inexplicable (04)
Michael, (05)
The major problem is that there is no document that precisely
defines the "aim of this group": (06)
> I do not think that it fits into the aim of this group. (07)
Following are three possible interpretations of the ONTAC goals: (08)
1. There shall be *one* single consistent theory that defines
*all* the predicates (or concept & relation types) that are
permissible in any message passed between any two systems
that claim to adhere to the ONTAC standards. (09)
2. There shall be a *family* of theories, each registered in a
metadata registry as specified by ISO 11179, and any message
passed between any two systems that adhere to the ONTAC
standards shall specify which theory or theories are assumed
to define the predicates that occur in that message. (010)
3. The theories specified in #2 shall consist of one central
core theory that is required and a family of optional
theories, each of which is consistent with the central
core. Any message passed between any two systems that
adhere to the ONTAC standards shall specify which theory
or theories are assumed *in addition to* the required core. (011)
After spending their first 5 years with interpretation #1, the
Cyc project abandoned it around 1990 in favor of interpretation #3.
I can't imagine that anybody seriously believes that the ONTAC WG
can accomplish what Cyc failed to do in anything less than the
21 years Cyc has already spent. (012)
Therefore, I believe that interpretation #3 is the only one we can
seriously contemplate on any reasonable time frame (i.e., something
considerably less than 21 years). Given that assumption, the main
questions to address are (013)
1. How big is the central core? What axioms shall be required? (014)
2. How do we relate the optional theories to one another and
to the central core? (015)
3. How do we handle messages passed between systems that use
different (and possibly inconsistent) optional theories? (016)
4. And most importantly, how will legacy systems communicate
with the new systems -- despite the fact that *none* of them
can be assumed to be consistent with the axioms of the core,
let alone the far more detailed axioms of the other theories? (017)
The point that I have been trying to make for the past five years
of the SUO project and the past 3 months of the ONTAC WG is that
unless these questions are addressed, there is no hope that any
of this effort will be of any value whatever to the people who
have day jobs working for managers who expect results. (018)
> ... we should at least agree on the language for specifying the
> ontologies. Common Logic seems a reasonable candidate for this
> purpose. (019)
I'm happy with that choice, but I also realize that the overwhelming
majority of the developers who will be expected to use the ONTAC WG
ontology are far more familiar with UML than with any CL dialect.
Even RDF and OWL are unfamiliar to most of them. (020)
> I was asking for a set of axioms in the language of FOL whose
> models are isomorphic to the model theory of pi calculus. (021)
You can represent pi calculus in FOL. Some axiomatizations may
use more exotic languages, but they're not required. (022)
In any case, I don't expect the programmers to master pi calculus.
But there are very widely used subsets of pi calculus that have
been used for years -- examples include PERT charts, UML activity
diagrams, Petri nets, etc. A major reason why the business
process modeling people have adopted pi calculus is that it is
the natural next step beyond what most programmers already know
-- namely PERT charts and UML activity diagrams (both of which
can easily be axiomatized in Common Logic). (023)
> But that's sort of my point -- how can pi calculus be a module
> if it is not specified as a set of axioms in the same language
> as every other module? (024)
I assume that there will be a *family* of theories of various levels
of detail, all of which can be axiomatized in some dialect of CL.
Translating PERT charts and UML activity diagrams into CL is trivial
compared to the task of teaching programmers PSL and situation
calculus. (025)
> ... There are many queries about processes that do not require
> explicitly using time, and you may want to answer queries about
> time without committing to all assumptions of a particular
> process ontology. If these two are too tightly coupled, you
> lose modularity, sharability and reusability. (026)
You are preaching to the choir. I have been trying to make the
point that the number of axioms required in the core should be
very small. In fact, the only consensus view about time is that
any notation should be translatable to UTC format. (027)
I would put all methods for reasoning about interactions between
time and processes into the optional modules -- that includes PSL,
PERT charts (as translated to some dialect of CL) and many other
versions that assume pi calculus or situation calculus or whatever. (028)
> Again, how can different modules be compared if they are written
> in different languages with different model theories. (029)
Excellent question. First, we could assume that all modules are
written in some dialect of Common Logic. Then we proceed as follows: (030)
http://www.jfsowa.com/logic/theories.htm
Theories, Models, Reasoning, Language, and Truth (031)
> ... but I thought that our objective here was to build some common
> ontologies, not reproduce the semantic integration problem. (032)
If a common ontology would magically solve all the problems, we could
just recommend Cyc and declare a victory. Cyc has been trying to do
that for 21 years without having anything that can pay the rent --
they still depend on government handouts for their continued existence. (033)
Unless we can provide a migration path for legacy systems, we have
done *nothing* that anybody would actually use. People are not going
to flip a switch tomorrow and magically have trillions of dollars of
software that conforms to whatever axioms the ONTAC WG proposes. (034)
> Given two first-order ontologies that intuitively cover the same
> concepts, you can try to find a weaker common theory such that both
> of the initial ontologies are consistent extension of the common
> theory. (035)
Yes, that is the recommendation of the theories.htm paper. (036)
> How do you hope to do this between pi calculus and any other
> first-order ontology of process? (037)
Some theories, such as PERT charts and Petri nets, are already
subsets of pi calculus. Others may have more complex mappings,
and the only common assumption might be that all times can be
translated to UTC format -- but that's not necessarily bad. (038)
For 99.97% of the databases in the world, the times recorded
in the DB do not include any information about how those times
were derived. That means, we can assume that messages that
assert event E happened at time T can be passed among systems
with no assumptions beyond the common core (i.e., that the
times can be translated to UTC format). (039)
Of course, more can and should be done, but version 1.0 must
be able to accommodate legacy systems before we can add new
features that really take advantage of the ontology. (040)
John (041)
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