Pat, (01)
Thanks for citing my papers. (02)
But I realize that there are a lot of different views and
axiomatizations of the notion of process. Following is a note
that I wrote to another forum, which summarizes the differences
between situation calculus and pi calculus (which includes
related systems, such as Petri nets and UML activity diagrams). (03)
Although I have my own preferences, I would recommend that none
of the detailed axioms be included in the upper level ontology
because different versions can be useful for different kinds of
problems. And I would suggest that *all* the major versions
be available in optional modules. (04)
The following note just illustrates the differences between
two major approaches, but many other versions have been and
undoubtedly will be invented. (05)
Some people have claimed that interoperabiliy is impossible
unless every system uses exactly the same axioms. But for
different problems, you can derive an answer about scheduling
and other time-dependent issues that can be represented by
low-level facts. Those facts can then be used by other systems
for other problems, even though different systems had derived
them under different assumptions. (06)
There are many complex issues involved, and for critical
problems, it may be necessary to see a complete trace of
the reasoning processes including all the original data.
But many applications just require one simple fact stated
as a UCT date/time. When we talk to people, we sometimes
need to ask how they arrived at the date, but very often
we just take the date as stated. The same is true of
computer systems. (07)
John Sowa
_______________________________________________________________ (08)
To illustrate various issues in reasoning about time and
processes, I'd like to summarize some of the critical points
that distinguish the situation calculus family and the
pi-calculus family (which includes Petri nets and some other
popular systems that are used in business process modeling): (09)
1. The formalization of situation calculus (as stated in
McCarthy's original papers) assumes a single *global*
situation at each instant of time. (010)
2. The pi-calculus family (which includes Petri nets and
several other notations) is formalized in terms of *local*
messages (AKA "tokens" in P-nets), and there is no
assumption of a global situation, a global clock, or any
global synchronization. (But it does not rule out the
option of synchronization by explicit message passing.) (011)
3. A formalism that defines processes in terms of a global
clock is a special case that assumes synchronization that
is unrealistic for many important applications and creates
unnecessary complications in reasoning. (012)
Sometimes a global clock is convenient, and we should permit
that assumption. But to make our approach more general, we
should also support other formalisms, including those that
focus on local message passing without any requirement for a
global clock. (013)
For more information about pi-calculus without all the hairy
formalism, I recommend the book on Business Process Modeling
by Michael Havey, published by O'Reilly. This book has a
chapter on pi-calculus and its relationships to various systems
used in BPM, but it's written for programmers rather than
mathematicians. (014)
Following is the O'Reilly web site: (015)
http://www.oreilly.com/catalog/essentialpm/ (016)
There is a sample chapter on that site, but unfortunately,
it's Chapter 2, and Chapter 3 is the one on pi-calculus. (017)
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