  Despite the extensive investment and impressive recent progress at reasoning
by similarity, deep learning continues to struggle with more complex forms of
reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is
a property of non-classical reasoning typically seen in commonsense reasoning,
whereby a reasoning system is allowed (differently from classical logic) to
jump to conclusions which may be retracted later, when new information becomes
available. Neural-symbolic systems such as Logic Tensor Networks (LTN) have
been shown to be effective at enabling deep neural networks to achieve
reasoning capabilities. In this paper, we show that by combining a
neural-symbolic system with methods from continual learning, LTN can obtain a
higher level of accuracy when addressing non-monotonic reasoning tasks.
Continual learning is added to LTNs by adopting a curriculum of learning from
knowledge and data with recall. We call this process Continual Reasoning, a new
methodology for the application of neural-symbolic systems to reasoning tasks.
Continual Reasoning is applied to a prototypical non-monotonic reasoning
problem as well as other reasoning examples. Experimentation is conducted to
compare and analyze the effects that different curriculum choices may have on
overall learning and reasoning results. Results indicate significant
improvement on the prototypical non-monotonic reasoning problem and a promising
outlook for the proposed approach on statistical relational learning examples.
