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The chase is a sound, complete, but possibly non-terminating algorithm for reasoning with existential rules (aka. tuple-generating dependencies), a highly expressive knowledge representation language. Although the procedure appears simple,…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
In order to handle the complexity and heterogeneity of mod- ern instruction set architectures, analysis platforms share a common design, the adoption of hardware-independent intermediate representa- tions. The usage of these platforms to…
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…
The Dafny verifier provides strong correctness guarantees but often requires numerous manual helper assertions, creating a significant barrier to adoption. We investigate the use of Large Language Models (LLMs) to automatically infer…
Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct…
Large language models (LLMs) have empowered AI agents to tackle increasingly complex tasks. However, most existing agents remain limited to static planning and brittle interactions, falling short of true collaboration or adaptive reasoning.…
Reasoning is an essential skill to enable Large Language Models (LLMs) to interact with the world. As tasks become more complex, they demand increasingly sophisticated and diverse reasoning capabilities for sequential decision-making,…
Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…
The Tactician's Web is a platform offering a large web of strongly interconnected, machine-checked, formal mathematical knowledge conveniently packaged for machine learning, analytics, and proof engineering. Built on top of the Coq proof…
Large language models (LLMs) are playing an increasingly important role in science and engineering. For example, their ability to parse and understand human and computer languages makes them powerful interpreters and their use in…
The General Intensional Programming System (GIPSY) has been built around the Lucid family of intensional programming languages that rely on the higher-order intensional logic (HOIL) to provide context-oriented multidimensional reasoning of…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
The use of a functional language to implement proof strategies as proof tactics in interactive theorem provers, often provides short, concise and elegant implementations. Whilst being elegant, the use of higher order features and combinator…
Sequential recommender systems have become increasingly important in real-world applications that model user behavior sequences to predict their preferences. However, existing sequential recommendation methods predominantly rely on…
Large Language Models (LLMs) have shown remarkable ability in solving complex tasks, making them a promising tool for enhancing tabular learning. However, existing LLM-based methods suffer from high resource requirements, suboptimal…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
The recent developments in Large Language Models (LLM), mark a significant moment in the research and development of social interactions with artificial agents. These agents are widely deployed in a variety of settings, with potential…