Related papers: ProofWatch: Watchlist Guidance for Large Theories …

Chain-of-thought explanations are widely used to inspect the decision process of large language models (LLMs) and to evaluate the trustworthiness of model outputs, making them important for effective collaboration between LLMs and humans.…

We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic…

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing…

Generalizable protein function prediction is increasingly constrained by the growing mismatch between exponentially expanding sequences of environmental proteins and the comparatively slow accumulation of experimentally verified functional…

I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…

Large language models (LLMs) have shown promise in formal theorem proving, but their token-level processing often fails to capture the inherent hierarchical nature of mathematical proofs. We introduce \textbf{Hierarchical Attention}, a…

Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning. While simple and effective, adding theory axioms can also pollute the search space with many irrelevant…

The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…

We present and verify template algorithms for lock-free concurrent search structures that cover a broad range of existing implementations based on lists and skiplists. Our linearizability proofs are fully mechanized in the concurrent…

Motivation: In silico methods for the prediction of antigenic peptides binding to MHC class I molecules play an increasingly important role in the identification of T-cell epitopes. Statistical and machine learning methods, in particular,…

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…

In this paper, we compare different existing approaches employed in data mining of big proof libraries in automated and interactive theorem proving.

Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…

Recommender systems are crucial tools to overcome the information overload brought about by the Internet. Rigorous tests are needed to establish to what extent sophisticated methods can improve the quality of the predictions. Here we…

We introduce Tinker, a tool for designing and evaluating proof strategies based on proof-strategy graphs, a formalism previously introduced by the authors. We represent proof strategies as open-graphs, which are directed graphs with…

As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…

We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…

Model checklists (Ribeiro et al., 2020) have emerged as a useful tool for understanding the behavior of LLMs, analogous to unit-testing in software engineering. However, despite datasets being a key determinant of model behavior, evaluating…

Large language models are evolving from single-turn responders into tool-using agents capable of sustained reasoning and decision-making for deep research. Prevailing systems adopt a linear pipeline of plan to search to write to a report,…