Related papers: A Survey on Theorem Provers in Formal Methods
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…
Recent work by Clark et al. (2020) shows that transformers can act as 'soft theorem provers' by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem…
Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
I argue that the most interesting goal facing researchers in automated reasoning is being able to solve problems that cannot currently be solved by existing tools and methods. This may appear obvious, and is clearly not an original thought,…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…