Related papers: Formalizing IMO Problems and Solutions in Isabelle…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics…
Interactive Machine Learning (IML) is an iterative learning process that tightly couples a human with a machine learner, which is widely used by researchers and practitioners to effectively solve a wide variety of real-world application…
This is an overview of the Isabelle technology behind the Archive of Formal Proofs (AFP). Interactive development and quasi-interactive build jobs impose significant demands of scalability on the logic (usually Isabelle/HOL), on Isabelle/ML…
The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems,…
The evolution of Artificial Intelligence (AI) has been significantly accelerated by advancements in Large Language Models (LLMs) and Large Multimodal Models (LMMs), gradually showcasing potential cognitive reasoning abilities in…
Large language models (LLMs) have achieved remarkable success in natural language processing tasks, yet their internal knowledge structures remain poorly understood. This study examines these structures through the lens of historical…
This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry…
Proof assistants offer tactics to facilitate inductive proofs. However, it still requires human ingenuity to decide what arguments to pass to those induction tactics. To automate this process, we present smart_induct for Isabelle/HOL. Given…
Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
The Isabelle/HOL proof assistant has a powerful library for continuous analysis, which provides the foundation for verification of hybrid systems. However, Isabelle lacks automated proof support for continuous artifacts, which means that…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof…
Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data…
Academic challenges comprise effective means for (i) advancing the state of the art, (ii) putting in the spotlight of a scientific community specific topics and problems, as well as (iii) closing the gap for under represented communities in…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…
We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…
Olympiad-level benchmarks in mathematics and physics are crucial testbeds for advanced AI reasoning, but chemistry, with its unique multimodal symbolic language, has remained an open challenge. We introduce ChemO, a new benchmark built from…