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.

翻译：尽管在基于相似性的推理方面投入了大量资源并取得了令人瞩目的最新进展，深度学习在更复杂的推理形式（如非单调推理和常识推理）上仍面临挑战。非单调性是非经典推理（通常见于常识推理）的一个特性，它允许推理系统（与经典逻辑不同）在获得新信息时，可能推翻先前得出的结论。神经符号系统（如逻辑张量网络LTN）已被证明能有效增强深度神经网络的推理能力。本文表明，通过将神经符号系统与持续学习方法相结合，LTN在处理非单调推理任务时能够获得更高的准确率。通过采用基于知识和数据的学习课程（含回顾机制），将持续学习引入LTN。我们将此过程称为“持续推理”，这是一种将神经符号系统应用于推理任务的新方法。持续推理被应用于一个典型的非单调推理问题以及其他推理示例。通过实验比较和分析了不同课程选择对整体学习与推理结果的影响。结果表明，该方法在典型非单调推理问题上取得了显著改进，并在统计关系学习示例中展现出良好的应用前景。