We propose a deep learning-based approach to the problem of premise selection: selecting mathematical statements relevant for proving a given conjecture. We represent a higher-order logic formula as a graph that is invariant to variable renaming but still fully preserves syntactic and semantic information. We then embed the graph into a vector via a novel embedding method that preserves the information of edge ordering. Our approach achieves state-of-the-art results on the HolStep dataset, improving the classification accuracy from 83% to 90.3%.

One of the fundamental challenges in reinforcement learning (RL) is to take a complex task and be able to decompose it to subtasks that are simpler for the RL agent to learn. In this paper, we report on our work that would identify subtasks by using some given positive and negative trajectories for solving the complex task. We assume that the states are represented by first-order predicate logic using which we devise a novel algorithm to identify the subtasks. Then we employ a Large Language Model (LLM) to generate first-order logic rule templates for achieving each subtask. Such rules were then further fined tuned to a rule-based policy via an Inductive Logic Programming (ILP)-based RL agent. Through experiments, we verify the accuracy of our algorithm in detecting subtasks which successfully detect all of the subtasks correctly. We also investigated the quality of the common-sense rules produced by the language model to achieve the subtasks. Our experiments show that our LLM-guided rule template generation can produce rules that are necessary for solving a subtask, which leads to solving complex tasks with fewer assumptions about predefined first-order logic predicates of the environment.

Logical reasoning systems are essential for rigorous automatic reasoning. The focus of the 2024 Logic and Practice of Programming workshop is integrating reasoning systems for trustworthy AI, especially including integrating diverse models of programming with rules and constraints. Trustworthy AI requires programming with rules and constraints for expressing and solving knowledge-intensive inference and combinatorial problems. A wide range of programming models have been proposed, including but not limited to the following, and essentially all of them require or support imperative programming for use in practical applications.

Game development is a highly technical practice that traditionally requires programming skills. This serves as a barrier to entry for would-be developers or those hoping to use games as part of their creative expression. While there have been prior game development tools focused on accessibility, they generally still require programming, or have major limitations in terms of the kinds of games they can make. In this paper we introduce Mechanic Maker, a tool for creating a wide-range of game mechanics without programming. It instead relies on a backend symbolic learning system to synthesize game mechanics from examples. We conducted a user study to evaluate the benefits of the tool for participants with a variety of programming and game development experience. Our results demonstrated that participants' ability to use the tool was unrelated to programming ability. We conclude that tools like ours could help democratize game development, making the practice accessible regardless of programming skills.

Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming (HPASP). Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on the performance. Sampling allows handling larger instances, but sometimes requires an increasing amount of memory.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks.

Probabilistic logical models are a core component of neurosymbolic AI and are important models in their own right for tasks that require high explainability. Unlike neural networks, logical models are often handcrafted using domain expertise, making their development costly and prone to errors. While there are algorithms that learn logical models from data, they are generally prohibitively expensive, limiting their applicability in real-world settings. In this work, we introduce precision and recall for logical rules and define their composition as rule utility -- a cost-effective measure to evaluate the predictive power of logical models. Further, we introduce SPECTRUM, a scalable framework for learning logical models from relational data. Its scalability derives from a linear-time algorithm that mines recurrent structures in the data along with a second algorithm that, using the cheap utility measure, efficiently ranks rules built from these structures. Moreover, we derive theoretical guarantees on the utility of the learnt logical model. As a result, SPECTRUM learns more accurate logical models orders of magnitude faster than previous methods on real-world datasets.

The remarkable advancements in artificial intelligence (AI), primarily driven by deep neural networks, are facing challenges surrounding unsustainable computational trajectories, limited robustness, and a lack of explainability. To develop next-generation cognitive AI systems, neuro-symbolic AI emerges as a promising paradigm, fusing neural and symbolic approaches to enhance interpretability, robustness, and trustworthiness, while facilitating learning from much less data. Recent neuro-symbolic systems have demonstrated great potential in collaborative human-AI scenarios with reasoning and cognitive capabilities. In this paper, we aim to understand the workload characteristics and potential architectures for neuro-symbolic AI. We first systematically categorize neuro-symbolic AI algorithms, and then experimentally evaluate and analyze them in terms of runtime, memory, computational operators, sparsity, and system characteristics on CPUs, GPUs, and edge SoCs. Our studies reveal that neuro-symbolic models suffer from inefficiencies on off-the-shelf hardware, due to the memory-bound nature of vector-symbolic and logical operations, complex flow control, data dependencies, sparsity variations, and limited scalability. Based on profiling insights, we suggest cross-layer optimization solutions and present a hardware acceleration case study for vector-symbolic architecture to improve the performance, efficiency, and scalability of neuro-symbolic computing. Finally, we discuss the challenges and potential future directions of neuro-symbolic AI from both system and architectural perspectives.

In the past few years, Large Language Models (LLMs) have exploded in usefulness and popularity for code generation tasks. However, LLMs still struggle with accuracy and are unsuitable for high-risk applications without additional oversight and verification. In particular, they perform poorly at generating code for highly complex systems, especially with unusual or out-of-sample logic. For such systems, verifying the code generated by the LLM may take longer than writing it by hand. We introduce a solution that divides the code generation into two parts; one to be handled by an LLM and one to be handled by formal methods-based program synthesis. We develop a benchmark to test our solution and show that our method allows the pipeline to solve problems previously intractable for LLM code generation.

In our previous research, we provided a reasoning system (called LeSAC) based on argumentation theory to provide legal support to designers during the design process. Building on this, this paper explores how to provide designers with effective explanations for their legally relevant design decisions. We extend the previous system for providing explanations by specifying norms and the key legal or ethical principles for justifying actions in normative contexts. Considering that first-order logic has strong expressive power, in the current paper we adopt a first-order deontic logic system with deontic operators and preferences. We illustrate the advantages and necessity of introducing deontic logic and designing explanations under LeSAC by modelling two cases in the context of autonomous driving. In particular, this paper also discusses the requirements of the updated LeSAC to guarantee rationality, and proves that a well-defined LeSAC can satisfy the rationality postulate for rule-based argumentation frameworks. This ensures the system's ability to provide coherent, legally valid explanations for complex design decisions.