Page 28 - Artificial Intelligence for the Internet of Everything

Introduction 15

CyberInfrastructure Group at NIST and is with the Carnegie Mellon Uni-
versity’s Engineering and Public Policy, Institute for Complex Engineered
Systems in Pittsburgh, PA. In this chapter the authors propose an argument
for the use of representations from category theory to support better models
for complex systems (to better understand the stability of mathematical
structures and as an alternative to set theory, “category” theory was devised
to consist of labeled directed subgraphs with arrows that associate, and
objects with unique arrows, such as A!B!C!A); the authors provide
examples of what an application of category theory might look like. Their
approach is based on the well-known observation that the design of complex
systems is fundamentally recursive, formalized in computer science with
structures known as algebras, coalgebras, and operads, 17 the mathematical
structures that happen to be closely linked to labeled tree representations.
Next, the authors construct two small examples from computer science
to illustrate the functional aspects and use of the categorical approach. Their
first example, a common HVAC heating and air conditioning system,
defines a logical semantics of contracts that they use to organize the different
requirements that may occur at the different scales in hierarchical systems.
The second example that the authors offer concerns the integration of AI
models into a preexisting human-driven process. The approach by the
authors is used by them to characterize the complexity of systems (e.g., het-
erogeneity, open interactions, multiple perspectives of jointly cognitive
agents). The authors conclude that category theory is hampered by the belief
held by others that it is too abstract and cumbersome, an obstacle that the
authors are striving to overcome by demonstrating its utility with the exam-
ples they provide and by concluding that the theory is well-linked across
many domains (e.g., physics, computer science, data science, etc.).
Chapter 14, titled “Meta-agents: Using Multiagent Networks to Manage
Dynamic Changes in the Internet of Things,” was written by Hesham
Fouad 18 and Ira S. Moskowitz of the Information Management and Deci-
sions Architecture Branch, Code 5580, at the Naval Research Laboratory
in Washington, DC. Fouad is a computer scientist with a strong background
in both academic research and commercial software development (e.g.,
SoundScape3D and VibeStation, used in the VR Laboratory at NRL);

17
To create reusable proofs, algebras provide a uniform language that generalize, for example, groups,
rings, lattices and monoids; coalgebras are duals used to represent classes and objects; and operads
model properties of mathematical structures of compositional architectures such as commutativity and
anti-commutativity (e.g., Jacobs, 2016).
18
Corresponding author: hesham.fouad@nrl.navy.mil.