Mills:
Interesting question, but I need to bound the response a little bit.....
If the focus of the integral framework (quads) is viewed as a "concept" then the quads and their respective aspects can be viewed as specific "contexts."
Formal concept analysis may then be directly applied. http://en.wikipedia.org/wiki/Formal_concept_analysis
There are aspects of formal concept analysis and lattice theory that may be applied across an wide range of topics using relations as one guiding filter.
Have fun,
Joe
On Sun, Jan 22, 2012 at 6:13 AM, Mills Davis <millsdavis@xxxxxxxxxxxxxx> wrote:
Jack Park & Jack Ring,
Do either of you know if there has been any rigorous application of Ken Wilber's integral theory for knowledge computing across disciplines? I recently came across a book entitled Integral Ecology — Uniting Perspectives on the Natural World, an 800-page tour-de-force by Esbjörn-Hargens and Zimmerman. Here is an excerpt from the intro. My sense is that there is a breakthrough waiting to happen here.
Mills Davis
On Jan 22, 2012, at 2:07 AM, Jack Ring wrote:
I think we can moderate the reductionism vs. holism divide once people comprehend the distinctions of class vs. type and learn to see both aspects of an object. Further, John Kineman's extension of Rosen's R-theory to a relational algebra seems quite promising. It occured to us back in the 1970's that in addition to set structural operators we also needed an algebra of sets. I think we are getting warmer.
Part of this may entail freeing thinkers from the von Neumann paradigm of stored program computers which makes people shy away from combinatorial constructs. Once people understand the recently patented General Purpose Set Theoretic Processor their conceptualization of 'the problem' may change considerably.
On Jan 21, 2012, at 4:01 PM, Debmacp wrote: That plus what should be processed by machines versus thought through by people
Deb
Sent from my iPhone
On Jan 21, 2012, at 4:27 PM, Jack Park <jackpark@xxxxxxxxx> wrote:
I think that there are some very powerful insights emerging in this
particular thread. For me, they edge ever closer to a boundary that
interest me greatly:
the boundary that separates machines from organisms.
That boundary is the same one that frequently emerges in conversations
that pit "reductionism" against holistic thinking.
I don't see reductionism and holism as necessarily being so orthogonal
that they get pitted against each other; as I see it, both are
necessary, but neither is sufficient. Sure, that point alone is well
worth its own conversation, but let me set that aside for a moment and
tell a short springboard story.
Nicholas Rashevski [1], considered the father of mathematical biology,
wrote a paper "Topology and life: In search of general mathematical
principles in biology and sociology" in 1954, which argued that for
all the math he invented, we still don't understand what makes
organisms tick. He launched the "relational biology" inquiry. He
sought a way to represent a "canonical organism". His student Robert
Rosen [2] eventually replaced Rashevski's graph and "organismic set"
approaches with category theory, and later wrote the book _Life
Itself_ which explains both the ontological and epistemological
grounds for his canonical organism representation, which entailed two
"components": metabolism and repair. Category theory showed that those
two entailed reproduction. What is important in this is the
observation that what is hard to represent are all of the necessary
"relationships" that exist between and among the components, and with
the external environment.
I offer that story as a suggestion that special consideration needs to
be given to relations. I will not suggest that more or less
consideration be given when weighed against the components being
modeled; I'll just leave it as a suggestion that relations in complex
systems -- organismic systems -- are important. Rosen was not able to
make graph or set theoretic approaches solve Rashevsky's quest;
Rashevsky died before Rosen realized a candidate solution, one rooted
in category theory.
I read it somewhere that while set theory lets you talk about members
of a set, category theory lets you talk about the social lives of
those members. I'm not smart enough to validate that, just smile.
JackP
Jack
[1] http://en.wikipedia.org/wiki/Nicolas_Rashevsky
[2] http://en.wikipedia.org/wiki/Robert_Rosen_%28theoretical_biologist%29
On Sat, Jan 21, 2012 at 8:31 AM, Deborah MacPherson <debmacp@xxxxxxxxx> wrote:
How to fix?
On Sat, Jan 21, 2012 at 10:19 AM, Jack Ring <jring7@xxxxxxxxx> wrote:
I suggest that this thread is beginning to highlight the absence of a
general semantics (Korsybski, Peirce, Bickerton, etc.) facet of the Summit.
The importance of this facet comes to the fore as big gets BIG then BIGGER.
General systems theory and practice are an insufficent basis. In the
traverse from a) an incorrect perception of a problem situation to z) the
self-sustaining operation of an intervention system that is exemplary in
quality, parsimony and beauty several languages will be used to express the
transformations and orchestrations of the numerous knowledge vectors as they
evolve.
Better fix this now.
Jack
On Jan 21, 2012, at 7:28 AM, k Goodier wrote:
Andrea,
Your note is exactly the kind of dialog I was hoping to get started.
It brings up what I believe is an important distinction for applied
ontology. In this case to engineered systems and to engineering of systems
(meta-engineering). The distinction is between the application, the language
used to talk about the application, and the specific knowledge (ontology)
represented within the language. OWL2 is a perfect place to discuss some
issues. OWL2 is not only an ontology language, but a formal ontology
language, and has the virtue that it has good reasoners. Starting from this
about 4 years ago I started looking at and attempting to use OWL2 for
representing product requirements and product designs. This starts in a
series of papers with among others Ian Horrocks, and David Leal. It clearly
is very promising. However, I have found that it is insufficient to
represent the semantics needed for concepts such as part-whole relations.
Certainly, one can introduce binary properties and call them part
properties. But the language without extensions is unable to do a good job
of representing a lot of engineering concepts. I am sure the ontologists
would concur. So for me it is not a question of throwing OWL out, it is what
semantic concepts are needed, how to express their semantics, and extensions
to OWL are needed. Also, by the way, as an engineer I have been very much
involved with using SysML to describe large scale systems and their
interaction with the world. I view SysML as an ontology language, albeit one
without a formal semantics. I also have been very much concerned with
retrofitting SysML with a formal semantics and adding OWL class and role
constructions. All to be able to build suitable ontologies for engineered
products and more recently biomedical systems such as the human heart.
- Henson
From: Westerinen, Andrea R. [mailto:ANDREA.R.WESTERINEN@xxxxxxxx]
Sent: Friday, January 20, 2012 12:06 PM
To: Ontology Summit 2011 discussion; henson.graves@xxxxxxxxxxx
Cc: Matthew West
Subject: RE: [ontology-summit] Summit Engineering Tracks
I have recently written a paragraph summarizing "why (OWL) ontologies?"
for a customer. It tries to address some of the points that Henson raises
below.
Here it is with the identifying text removed:
Xxx requires the analysis, communication, comparison and [alignment]
of [concepts] within and across authoritative tiers, addressing broad
(high-level) to specific (low-level) enterprise environments. These
requirements necessitate the creation of formal, semantically
enabled models [of the concepts], and their identifying and supporting
properties, relationships and individuals. Providing both a formal
encoding and semantic richness allows normalization of the definitions
(intent) and provides the ability to aggregate, compare, and reason over the
[concepts]. These tasks and requirements are well-aligned to the goals and
capabilities of an ontology-based approach. Ontologies, defined using W3C's
OWL, can be created, stored and reasoned over using COTS tooling. In
addition, many complementary supporting ontologies can be immediately
imported, aligned and reused (such as the provenance and time/event
ontologies from W3C, an ISO-3166 country ontology at downlode.org,
and specific domain ontologies such as Xxx). Even if existing data is not
in an ontological format, but is perhaps stored as a relational database,
there is existing tooling to convert this data to an RDF encoding. (Taking
this approach removes the need to use complex staging tables to mediate
database information.) Using an OWL ontology as the basis for the Xxx Model
allows the formalization of not only the core concepts (...) but also puts
strong focus on the relationships between these concepts and the definition
of formal-logic-based restrictions, facts/axioms, and rules. Using COTS
OWL reasoners, logical analyses of the consistency, completeness and minimal
set definitions are straightforward, along with the ability to align
concepts and infer new data based on logical expressions and if/then (Horn)
rules. Communication of a standardized, ontological, machine-understandable
format [to environment-specific] translation agents will produce
consistent, traceable and auditable definitions for specific end-point
implementations.
Andrea Westerinen
| SAIC - CISBU | Sr Technical Expert | westerinena@xxxxxxxx | bb
425-281-3611
________________________________
From: henson graves [mailto:henson.graves@xxxxxxxxxxx]
Sent: Fri 1/20/2012 9:00 AM
To: 'Ontology Summit 2011 discussion'
Cc: 'Matthew West'
Subject: [ontology-summit] Summit Engineering Tracks
The track co-champions are soliciting input, participation, and
references
for the two tracks on engineering of large systems and the resulting
engineered systems.
My interest for the engineering tracks is to establish dialog in the
Summit
not only to identify engineering problems for which ontology can offer
solutions. But to go beyond that to dialog on what ontology results and
methodology can be applied and look at use cases for its application. Many
people in the industry of developing and using engineered systems are
aware
that ontology may provide value to many of their problems and issues. But
the industry position is what ontology technology can help, how do we use
it, what are the benefits, and what will it cost. At least this has always
been the management response when I have taken proposals regarding
ontology
forward in industry.
If this did not go to the general interest list, someone give me a pointer
to the right one.
- Henson Graves
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