Systems, Man & Cybernetics - July 2015 - 13

hierarchy of neural populations with collective dynamics and higher cognition. There is a hierarchy of K-sets
that describes various levels of cortical structures and
corresponding cognitive functions [27]. At the top level,
we have the fourth-order Katchalsky set (KIV) set, which
describes the structure of the cortical hemisphere, combining multisensory signal processing into the intentional
action-perception cycle with intermittent synchronization/
desynchronization transitions correlated with awareness
experience [10], [28]. Various aspects of the KIV model
include encoding of the meaning of sensory stimuli based
on the subject's past experiences and present intentions. The
corresponding activity patterns lead to awareness experience in the form of multisensory percepts [28].
An embedded robotics paradigm has been outlined
to construct artificial systems with awareness based on
dynamical principles [27]. These results provide guidelines to design decision support systems with the degree
of situational awareness and robust operation in changing environmental conditions. The application areas will
include aware systems with rapid response in emergency
scenarios and natural disasters, and cognitive robotics
for serving the elderly at home and at medical facilities.
As shown in Figure  1, the NASA Mars Rover prototype
provides an example of an embedded robotics test bed
with autonomous learning and navigation capabilities.
A Three-Valued Logic Model
of Aware Systems
There are two complementary and mutually beneficial
approaches to understand the awareness mechanisms:
1) to investigate the working of the brain and 2) to build
abstract mathematical and computational models. We have
discussed the first approach in the "Awareness: Sometimes
an Enigma" and "Neural Correlates and Dynamical Models
of Awareness" sections. In this section, we consider the second one [29], which is a high-level description of awareness
using the abstract mathematical tool of directed graphs.
In general, an aware system can be defined as a directed acyclic graph G ^V, E h, where V is a set of nodes (vertices) and E 3 V # V is a set of edges (connections or arcs).
Each node in V is a lower level aware system, and an edge
from the ith node v i to the jth node v j means v i provides some information that will be useful for v j to make
decisions. Loop is not allowed (at least for a certain time
instance) because of the causality.
Since each node is also an aware system, aware systems can be defined recursively in a similar way defining
logic expressions. At the beginning, we have some prime
or atomic aware systems that cannot be decomposed further. We call a prime aware system an aware unit (AU). An
AU is an aware system in which V contains only one node
and E is empty. Thus, we have the following definition.
◆ Any AU is an aware system.
◆ If V is a set of aware systems with V 2 1, then the
directed acyclic graph G ^V, E h is also an aware sys-

tem, where E 3 V # V is any set of edges that makes
G a legal directed acyclic graph.
Note that, although an AU has only one node, it contains connectors in both input and output sides, so that
many AUs can be connected to form a higher level aware
system. In addition, to make the system meaningful, the
graph should be connected. Furthermore, since the aware
system defined above has a nested structure, it will be
very difficult to understand the system structure and analyze the system behavior. One convenient way to solve this
problem is to assume that each subsystem is capsulated
and defines only one concept. In addition, we assume that
a subsystem is defined as follows:
f (x) 2 Tu
1,
y = * 0, Tl 1 f (x) # Tu
- 1,
f (x) # Tl,

(1)

where x ! U is an observed pattern, in which U is the
universe (or the feature space containing all possible
patterns); f ( ) is an aware function; and Tl and Tu are,
respectively, the lower and upper alert levels, which are
the thresholds for the system to become aware. The input
x is (or can be converted into) an n- dimensional vector
of numbers, and the output y is a scalar.
The concept C defined by each subsystem is a subset
of 2 U . If the output y is 1, the input x definitely belongs
to C. If y is -1, x definitely does not belong to C. If y
is 0, the subsystem cannot make the decision. In other
words, the subsystem is aware if y is 1 or -1; otherwise,
the subsystem is unaware. Thus, each subsystem in an
aware system is a three-valued logic operator. Besides
accept and reject, the subsystem also makes an unknown
decision. The basic concern here is that a subsystem
should make a decision only when it is aware and should
not make any decision if it is unaware.
The well-known McCulloch-Pitts neuron can be used
to define an AU. Here, the aware function f ^ x h is a bipolar
sigmoid function, x is the effective input, and Tl and Tu
can take values from [-1,0] to [0,1], respectively. To define
Table 1. One of the results
for *the XOR problem.
Error after the 1,345th iteration = 0.00995
Parameters for the output layer:
1.23137 1.31276 -0.74332
Parameters for the hidden layer:
-0.44280 0.41387 0.07437
0.96318 -0.52348 0.97266
Truth values of all neurons:
In1
-1
-1
1
1

In2 H1 H2 Out
-1 0 -1 -1
1 1 -1 1
-1 -1
1 1
1 0 -1 -1

Ju ly 2 01 5

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Table of Contents for the Digital Edition of Systems, Man & Cybernetics - July 2015

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