Neuro-Symbolic AI Approaches to Enhance Deep Neural Networks with Logical Reasoning and Knowledge Integration

One of the challenges in Artificial Intelligence (AI) is to integrate fast, automatic, and intuitive System-1 thinking with slow, deliberate, and logical System-2 thinking. While deep learning approaches excel at perception tasks for System-1, their reasoning capabilities for System-2 are limited. Besides, deep learning approaches are usually data-hungry, hard to make use of explicit knowledge, and struggling with interpretability and justification. This dissertation presents three neuro-symbolic AI approaches that integrate neural networks (NNs) with symbolic AI methods to address these issues. The first approach presented in this dissertation is NeurASP, which combines NNs with Answer Set Programming (ASP), a logic programming formalism. NeurASP provides an effective way to integrate sub-symbolic and symbolic computation by treating NN outputs as probability distributions over atomic facts in ASP. The explicit knowledge encoded in ASP corrects mistakes in NN outputs and allows for better training with less data. To avoid NeurASP's bottleneck in symbolic computation, this dissertation presents a Constraint Loss via Straight-Through Estimators (CL-STE). CL-STE provides a systematic way to compile discrete logical constraints into a loss function over discretized NN outputs and scales significantly better than state-of-the-art neuro-symbolic methods. This dissertation also presents a finding when CL-STE was applied to Transformers. Transformers can be extended with recurrence to enhance its power for multi-step reasoning. Such Recurrent Transformer can straightforwardly be applied to visual constraint reasoning problems while successfully addressing the symbol grounding problem. Lastly, this dissertation addresses the limitation of pre-trained Large Language Models (LLMs) on multi-step logical reasoning problems with a dual-process neuro-symbolic reasoning system called LLM+ASP, where an LLM (e.g., GPT-3) serves as a highly effective few-shot semantic parser that turns natural language sentences into a logical form that can be used as input to ASP. LLM+ASP achieves state-of-the-art performance on several textual reasoning benchmarks and can handle robot planning tasks that an LLM alone fails to solve.