Related papers: Learning to Prove Theorems by Learning to Generate…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
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…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
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…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
Humans can develop new theorems to explore broader and more complex mathematical results. While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new…
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…
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…
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,…
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…
Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…
Automatic generation of paraphrases from a given sentence is an important yet challenging task in natural language processing (NLP), and plays a key role in a number of applications such as question answering, search, and dialogue. In this…
Inspired by the recent evolution of deep neural networks (DNNs) in machine learning, we explore their application to PL-related topics. This paper is the first step towards this goal; we propose a proof-synthesis method for the…