A New Perspective for Risk Management: A Study of the Design of Generic Technology with a Matroid Model in C-K Theory - Principia Designae: Pre-Design, Design, and Post-Design - page 203

The model also enlightens some aspects of “independence” in generic
technologies:
1. The design of GT actually establishes a certain structure between designed world
and environment. Here this independence is actually modeled as a complete
graph K n-1 . One can underline that in terms of matroids, this structure has
interesting properties: K n-1 and U n,n have the same rank; one can even notice
that their lattice of flat are isomorph (see (Oxley 2011 ) ); but they have very
different corank, 0 zero for U n,n and (n-1)(n-2)/2 for K n-1 and hence very
different dependent sets. This means that a generic technology appears as a
set of compatible, more or less substitutable technologies. In a sense the knowl-
edge set of an engineering department should embody a generic technology!
2. Note that the design process actually works on several structures: two structures
in K, modeling what is known; and also a structure in C. The latter is interesting:
this is the structure of the unknown! This structure represents all the “holes” in K
and their interdependences. The design consists in building this structure and
“extracting” some edges from it to make them become knowledge. It can be
noted that the C-structure follows a matroid structure which enables a relatively
easy process to identify a spanning tree in the C-graph.
13.4 Part 3: Dynamic Models of the Interaction Designed
World/Environment
Based on the model above, we can now study the dynamic interaction between a
designed world and some “constraints”.
13.4.1 Dynamic Model
As already noticed in part 1, the logic of generic technology leads to a new logic to
follow the dynamics of context. As long as a new “context” is actually a dependent
set in the structure of external structures, then this context is taken into account by
the generic technology. Hence the only change in context that would lead to a
new design are context that include a property that is independent from the past F.
It can be a new function f n+1 .
In a dynamic process, this kind of extension might lead to several forms:
1. If the successive sets of risks F(t) are included one after the other (for each t,
F(t) F(t + 1)), then the process leads at each time t to a complete matroid
K(t) with K(t) F(t + 1)
2. But there is another possibility: suppose that the set F(t + 1) contains a new
function f t+1 but does not contain all previous functions. Then in C, edges that
are known and not necessary are deleted. By decreasing the requests for