Page 266 - Artificial Intelligence for the Internet of Everything

244 Artificial Intelligence for the Internet of Everything

of engineered systems. Our approach, as previously mentioned, is that sys-
tem design is a fundamentally recursive process, including a decompositional
phase that identifies components and their requirements and a compositional
phase of integration and testing. With this in mind we recall the theory func-
torial algebras and coalgebras, categorical datatypes for representing recur-
sive structures based using labeled trees.
To fit our analysis to this approach, we must encode the architecture of a
system into the labels of a tree. To this end we introduce a second class of
categorical constructs called operads. Roughly speaking, an operad describes
a class of possible architectures; for example, we might describe physical,
logical, and hybrid systems using three different operads. The architectural
rules in these worlds may be different since, for example, logical resources
can be broadcast (one-to-many interaction) whereas physical ones cannot.
Based on these architectures we can assign various types of semantics to
our system representations. To illustrate this point, we will give an example
of logical semantics that captures the relationships between system and com-
ponent requirements. This example can be seen as the prelude to the more
sophisticated semantics that will be needed to describe other elements of the
system-design process including models, designs, and testing procedures.
We close with a discussion of how these representations can support and
constrain new applications of AI at different levels of abstraction.

13.2 CHARACTERISTICS OF COMPLEX SYSTEMS

In this section we review some common features that we expect to find in
contemporary complex systems. We will not attempt to define complexity
here, and in fact caution against a reductive definition of the term. For exam-
ple, some have equated complexity with heterogeneity, our first listed char-
acteristic, but this is only one relevant axis of complexity (scale being
another) (Mitchell, 2009). We do not demand that a given complex system
display all of these features, though some will, but most are likely to exhibit
at least one or two. In particular, any attempt to provide generic structures
for system representations across a variety of domains and use-cases will need
to be able to handle all of these considerations.

13.2.1 Heterogeneity of Components

In modern systems the component elements may include, at a minimum,
human actors and subjects, “dumb” physical components, “smart” con-
nected devices, and cloud services. This indicates that to understand, predict,