NeurASP: Embracing Neural Networks into Answer Set Programming

We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation. We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set programming. Also, NeurASP can be used to train a neural network better by training with ASP rules so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by the rules.

Leveraging Large Language Models to Generate Answer Set Programs

Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning capabilities are limited and relatively shallow, despite the application of various prompting techniques. In contrast, formal logic is adept at handling complex reasoning, but translating natural language descriptions into formal logic is a challenging task that non-experts struggle with. This paper proposes a neuro-symbolic method that combines the strengths of large language models and answer set programming. Specifically, we employ an LLM to transform natural language descriptions of logic puzzles into answer set programs. We carefully design prompts for an LLM to convert natural language descriptions into answer set programs in a step by step manner. Surprisingly, with just a few in-context learning examples, LLMs can generate reasonably complex answer set programs. The majority of errors made are relatively simple and can be easily corrected by humans, thus enabling LLMs to effectively assist in the creation of answer set programs.

Coupling Large Language Models with Logic Programming for Robust and General Reasoning from Text

While large language models (LLMs), such as GPT-3, appear to be robust and general, their reasoning ability is not at a level to compete with the best models trained for specific natural language reasoning problems. In this study, we observe that a large language model can serve as a highly effective few-shot semantic parser. It can convert natural language sentences into a logical form that serves as input for answer set programs, a logic-based declarative knowledge representation formalism. The combination results in a robust and general system that can handle multiple question-answering tasks without requiring retraining for each new task. It only needs a few examples to guide the LLM's adaptation to a specific task, along with reusable ASP knowledge modules that can be applied to multiple tasks. We demonstrate that this method achieves state-of-the-art performance on several NLP benchmarks, including bAbI, StepGame, CLUTRR, and gSCAN. Additionally, it successfully tackles robot planning tasks that an LLM alone fails to solve.

Learning to Solve Constraint Satisfaction Problems with Recurrent Transformer

Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner, having clear advantages over state-of-the-art methods such as Graph Neural Networks, SATNet, and some neuro-symbolic models. With the ability of Transformer to handle visual input, the proposed Recurrent Transformer can straightforwardly be applied to visual constraint reasoning problems while successfully addressing the symbol grounding problem. We also show how to leverage deductive knowledge of discrete constraints in the Transformer's inductive learning to achieve sample-efficient learning and semi-supervised learning for CSPs.

Injecting Logical Constraints into Neural Networks via Straight-Through Estimators

Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning. More specifically, we design a systematic way to represent discrete logical constraints as a loss function; minimizing this loss using gradient descent via a straight-through-estimator updates the neural network's weights in the direction that the binarized outputs satisfy the logical constraints. The experimental results show that by leveraging GPUs and batch training, this method scales significantly better than existing neuro-symbolic methods that require heavy symbolic computation for computing gradients. Also, we demonstrate that our method applies to different types of neural networks, such as MLP, CNN, and GNN, making them learn with no or fewer labeled data by learning directly from known constraints.

Extending Answer Set Programs with Neural Networks

The integration of low-level perception with high-level reasoning is one of the oldest problems in Artificial Intelligence. Recently, several proposals were made to implement the reasoning process in complex neural network architectures. While these works aim at extending neural networks with the capability of reasoning, a natural question that we consider is: can we extend answer set programs with neural networks to allow complex and high-level reasoning on neural network outputs? As a preliminary result, we propose NeurASP -- a simple extension of answer set programs by embracing neural networks where neural network outputs are treated as probability distributions over atomic facts in answer set programs. We show that NeurASP can not only improve the perception accuracy of a pre-trained neural network, but also help to train a neural network better by giving restrictions through logic rules. However, training with NeurASP would take much more time than pure neural network training due to the internal use of a symbolic reasoning engine. For future work, we plan to investigate the potential ways to solve the scalability issue of NeurASP. One potential way is to embed logic programs directly in neural networks. On this route, we plan to first design a SAT solver using neural networks, then extend such a solver to allow logic programs.

Translating LPOD and CR-Prolog2 into Standard Answer Set Programs

Logic Programs with Ordered Disjunction (LPOD) is an extension of standard answer set programs to handle preference using the construct of ordered disjunction, and CR-Prolog2 is an extension of standard answer set programs with consistency restoring rules and LPOD-like ordered disjunction. We present reductions of each of these languages into the standard ASP language, which gives us an alternative way to understand the extensions in terms of the standard ASP language.