Page 290 - Artificial Intelligence for the Internet of Everything

268 Artificial Intelligence for the Internet of Everything

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Fig. 13.4 A categorical model in the style of a unified modeling language class diagram
(Breiner, Padi, et al., 2017).

chapter, sketches can be presented graphically, allowing us to design math-
ematical models using techniques that are very similar to existing methods
like class diagrams in the Systems Modeling Language. See Fig. 13.4 for an
example and Breiner, Padi, Subrahmanian, and Sriram (2017) for a detailed
exposition.
Another crucial characteristic of CT for systems modeling is its self-
referentiality. We can think of categories  and  themselves as (informa-
tional) resources, and functors as processes that operate on them, providing
concrete translations between different information representations. This
allows us to bridge different information models, providing the means to
manage and integrate the many perspectives found in any complex system.
Sometimes these transformations will be bidirectional, providing a dic-
tionary between one and the other; this could already be quite useful for data
wrangling. More interesting, though, are cases in which the transformation
cannot be reversed. In Breiner, Subrahmanian, and Jones (2017) the authors
showed that functors can be used to relate architectures at different levels of
abstraction, so that one category gives a functional refinement of another.
This allowed us to give a unified approach to process modeling from the
production line to the factory to the global supply chain.
In other cases,  might contain additional information that must be
projected out in the passage to . This might be the case, for example, if 
contains a simple process model that is extended in  to include security
concerns by explicitly representing resources like encryption keys.
Finally, we note that the burden of joint cognition is mitigated somewhat
bythediagrammaticcharacterofCT.Unlikemostformaldisciplines,CTuses
diagrams extensively as tools for simplifying complex arguments. We have
already seen the use of trees and graphs to model different elements of systems