Results 211 to 220 of about 1,881,310 (251)

Solving Formal Math Problems by Decomposition and Iterative Reflection

arXiv.org
General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning.
Yichi Zhou, Jianqiu Zhao, Yongxin Zhang, Bohan Wang, Siran Wang, Luoxin Chen, Jiahui Wang, Haowei Chen, Allan Jie, Xinbo Zhang, Haocheng Wang, L. Trung, Rong Ye, Phan Nhat Hoang, Huishuai Zhang, Peng Sun, Hang Li   +16 more
semanticscholar   +1 more source

Prover Agent: An Agent-based Framework for Formal Mathematical Proofs

arXiv.org
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean.
Kaito Baba, Chaoran Liu, Shuhei Kurita, Akiyoshi Sannai   +3 more
semanticscholar   +1 more source

Cooperative Repositories for Formal Proofs

2007
We present a new framework for the online development of formalized mathematics. This framework allows wiki-style collaboration while providing users with a rendered and browsable version of their work. We describe a prototype based on Coq, its web interface as implemented by the second author, and a modified version of the MediaWiki code-base.
Pierre Corbineau, Cezary Kaliszyk
openaire   +1 more source

Annotations in formal specifications and proofs

Formal Methods in System Design, 1994
In order to exploit the connection between the formal and the informal aspects of modeling, the author proposes a system of annotations that can be used to incorporate semantic information concerning the domain being reasoned about into a formal proof environment. Annotations will serve as comments, labels, or proof directives. An implementation in the
openaire   +2 more sources

Formal Mathematical Reasoning: A New Frontier in AI

arXiv.org
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large language models ...
Kaiyu Yang, Gabriel Poesia, Jingxuan He, Wenda Li, Kristin E. Lauter, Swarat Chaudhuri, Dawn Song   +6 more
semanticscholar   +1 more source

MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data

International Conference on Learning Representations
Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring
Yinya Huang, Xiaohan Lin, Zhengying Liu, Qingxing Cao, Huajian Xin, Haiming Wang, Zhenguo Li, Linqi Song, Xiaodan Liang   +8 more
semanticscholar   +1 more source

Formalizing the Proof of the Kepler Conjecture

2004
The Kepler Conjecture states that the densest packing of spheres in three dimensions is the familiar cannonball arrangement. Although this statement has been regarded as obvious by chemists, a rigorous mathematical proof of this fact was not obtained until 1998.
openaire   +1 more source

The translation of formal proofs into English

Artificial Intelligence, 1976
Abstract The argument of a logical proof written up in English can be represented by a formal proof in symbolic logic; this formal proof can also be taken to represent the deep structure of the written proof. This paper describes a program which generates a written proof from such a representation.
openaire   +2 more sources

Automated Proof Generation for Rust Code via Self-Evolution

International Conference on Learning Representations
Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation.
Tianyu Chen, Shuai Lu, Shan Lu, Yeyun Gong, Chenyuan Yang, Xuheng Li, Md Rakib Hossain Misu, Hao Yu, Nan Duan, Peng Cheng, Fan Yang, Shuvendu K. Lahiri, Tao Xie, Lidong Zhou   +13 more
semanticscholar   +1 more source

On formal specification of a proof tool

1991
Tools and methods for the specification and design of computer systems are increasing in sophistication. Much current research and development is attempting to exploit this sophistication to improve the effectiveness of systems development practices.
openaire   +1 more source