  The human reasoning process is seldom a one-way process from an input leading
to an output. Instead, it often involves a systematic deduction by ruling out
other possible outcomes as a self-checking mechanism. In this paper, we
describe the design of a hybrid neural network for logical learning that is
similar to the human reasoning through the introduction of an auxiliary input,
namely the indicators, that act as the hints to suggest logical outcomes. We
generate these indicators by digging into the hidden information buried
underneath the original training data for direct or indirect suggestions. We
used the MNIST data to demonstrate the design and use of these indicators in a
convolutional neural network. We trained a series of such hybrid neural
networks with variations of the indicators. Our results show that these hybrid
neural networks are very robust in generating logical outcomes with inherently
higher prediction accuracy than the direct use of the original input and output
in apparent models. Such improved predictability with reassured logical
confidence is obtained through the exhaustion of all possible indicators to
rule out all illogical outcomes, which is not available in the apparent models.
Our logical learning process can effectively cope with the unknown unknowns
using a full exploitation of all existing knowledge available for learning. The
design and implementation of the hints, namely the indicators, become an
essential part of artificial intelligence for logical learning. We also
introduce an ongoing application setup for this hybrid neural network in an
autonomous grasping robot, namely as_DeepClaw, aiming at learning an optimized
grasping pose through logical learning.
