Knowledge Sharing Core
. KSF-Report .
Communication
to the Natural Science & Mathematics Communities
In science a notational system is for
communication. We use a highly formalized
language designed to support science of knowledge creation, sharing and
management. [*]
Differential ontology framework was designed to
measure stochastic structure and convert this structure to a collection of
discrete elements, in this case a specific graph structure with node values
occurring or having been inferred as afforded by the structure of invariance
within the data.
The term “affordance” is used first by J.J.
Gibson in the foundations of an academic discipline called “ecological
physics”. This term is one of those
that are essential within an objective discussion about knowledge creation,
sharing and management. In the
knowledge sciences, one also has to account for the differences between viewpoint
and the difference between private experience and shared experiences. One way to approach these differences is in
a separate delineation of function and structure. In linguistics this differentiation between descriptions of
function and of structure is called double articulation.
We are conjecturing that class:object
pairing is the proper way to discuss the relationship between function and
structure, and is perhaps optimal in terminological use for modeling complex
systems where structure is differentially shaped by the functional needs of an
environment.
The indeterminacy seen in function/structure
descriptions has not been precisely captured by Hilbert (or “classical”) mathematics. In computer science we find open problems
related to the halting conditions. In
mathematical biology we find that the more mathematics is used in a strict since,
the less biology we study.
For us, it has seemed appropriate to create a
new stratified mathematics with the Hilbert space mathematics as the
"crisp" expression.
In the non-crisp form we have a tri-level
architecture and both differential ontology and formative ontology. But still open problems remain.
Artificial neural networks, of the more advanced
form from the Stephen Grossberg school, can be used within each level to create
process dynamics governed by first order differential equations, as models
providing adaptive selection and categorization, or first order predicate
logics.
Here is the question that might be asked and answered by the group, and by leading scholars and policy makers.
“Fundamental
question: Do
we wish to reinforce the notion that class exists at one level of informational
organization and localized informational objects exists at a different level of
informational organization?
If
the answer to this fundamental question is yes, then we must develop the theory
of Human-centric Information Production (HIP) in a way that is consistent with the
notions of "cross scale transforms" that
1: creates localized "units" of
information from some global measurement, and
2: aggregates collections of these localized
units of information into a global organization (or schema) in a formative
fashion
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