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Related papers: Sharing HOL4 and HOL Light proof knowledge

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Demonstration learning aims to guide the prompt prediction via providing answered demonstrations in the few shot settings. Despite achieving promising results, existing work only concatenates the answered examples as demonstrations to the…

Machine Learning · Computer Science 2022-09-02 Sirui Wang , Kaiwen Wei , Hongzhi Zhang , Yuntao Li , Wei Wu

Automated theorem proving (ATP) has been a classical problem in artificial intelligence since its inception, yet it remains challenging due to its vast state and action space. Large language models (LLMs) have recently emerged as a…

Machine Learning · Computer Science 2025-07-22 Matěj Kripner , Michal Šustr , Milan Straka

Proof assistants enable users to develop machine-checked proofs regarding software-related properties. Unfortunately, the interactive nature of these proof assistants imposes most of the proof burden on the user, making formal verification…

Software Engineering · Computer Science 2024-05-08 Pedro Carrott , Nuno Saavedra , Kyle Thompson , Sorin Lerner , João F. Ferreira , Emily First

While Large Language Models (LLMs) have demonstrated strong math reasoning abilities through Reinforcement Learning with *Verifiable Rewards* (RLVR), many advanced mathematical problems are proof-based, with no guaranteed way to determine…

Computation and Language · Computer Science 2026-02-20 Haotong Yang , Zitong Wang , Shijia Kang , Siqi Yang , Wenkai Yu , Xu Niu , Yike Sun , Yi Hu , Zhouchen Lin , Muhan Zhang

Hammers are tools that provide general purpose automation for formal proof assistants. Despite the gaining popularity of the more advanced versions of type theory, there are no hammers for such systems. We present an extension of the…

Logic in Computer Science · Computer Science 2016-06-21 Łukasz Czajka , Cezary Kaliszyk

Logical reasoning is a core challenge in natural language understanding and a fundamental capability of artificial intelligence, underpinning scientific discovery, mathematical theorem proving, and complex decision-making. Despite the…

Computation and Language · Computer Science 2025-12-04 Qingchuan Li , Mingyue Cheng , Zirui Liu , Daoyu Wang , Yuting Zeng , Tongxuan Liu

Humans can quickly learn new visual concepts, perhaps because they can easily visualize or imagine what novel objects look like from different views. Incorporating this ability to hallucinate novel instances of new concepts might help…

Computer Vision and Pattern Recognition · Computer Science 2018-04-04 Yu-Xiong Wang , Ross Girshick , Martial Hebert , Bharath Hariharan

We present a new approach to integrating deep learning with knowledge-based systems that we believe shows promise. Our approach seeks to emulate reasoning structure, which can be inspected part-way through, rather than simply learning…

Artificial Intelligence · Computer Science 2019-12-12 Aaron Eberhart , Monireh Ebrahimi , Lu Zhou , Cogan Shimizu , Pascal Hitzler

Artificial Intelligence (AI) has increasingly influenced modern society, recently in particular through significant advancements in Large Language Models (LLMs). However, high computational and storage demands of LLMs still limit their…

Computation and Language · Computer Science 2025-04-23 Daniel Hendriks , Philipp Spitzer , Niklas Kühl , Gerhard Satzger

The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…

Logic in Computer Science · Computer Science 2018-09-10 Artem Yushkovskiy

We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…

Logic in Computer Science · Computer Science 2024-03-21 Simon Guilloud , Sankalp Gambhir , Andrea Gilot , Viktor Kunčak

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…

Computation and Language · Computer Science 2024-12-18 Vernon Y. H. Toh , Deepanway Ghosal , Soujanya Poria

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type…

Logic in Computer Science · Computer Science 2019-11-20 Chad E. Brown , Thibault Gauthier , Cezary Kaliszyk , Geoff Sutcliffe , Josef Urban

Concerns regarding the propensity of Large Language Models (LLMs) to produce inaccurate outputs, also known as hallucinations, have escalated. Detecting them is vital for ensuring the reliability of applications relying on LLM-generated…

Computation and Language · Computer Science 2024-05-31 Ernesto Quevedo , Jorge Yero , Rachel Koerner , Pablo Rivas , Tomas Cerny

There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…

Logic in Computer Science · Computer Science 2021-10-19 Wesley H. Holliday , Chase Norman , Eric Pacuit

Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…

Computation and Language · Computer Science 2021-08-03 Siyuan Wang , Zhongkun Liu , Wanjun Zhong , Ming Zhou , Zhongyu Wei , Zhumin Chen , Nan Duan

Large language models (LLMs) have demonstrated their potential to refine their generation based on their own feedback. However, the feedback from LLM itself is often inaccurate, thereby limiting its benefits. In this paper, we propose Study…

Computation and Language · Computer Science 2023-10-25 Danqing Wang , Lei Li

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…

Machine Learning · Computer Science 2026-03-05 Manooshree Patel , Rayna Bhattacharyya , Thomas Lu , Arnav Mehta , Niels Voss , Narges Norouzi , Gireeja Ranade

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…

Artificial Intelligence · Computer Science 2026-03-05 Manooshree Patel , Rayna Bhattacharyya , Thomas Lu , Arnav Mehta , Niels Voss , Narges Norouzi , Gireeja Ranade

In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…

Logic in Computer Science · Computer Science 2021-07-07 Quentin Garchery