Related papers: PRover: Proof Generation for Interpretable Reasoni…

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…

Most AI systems are black boxes generating reasonable outputs for given inputs. Some domains, however, have explainability and trustworthiness requirements that cannot be directly met by these approaches. Various methods have therefore been…

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…

We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…

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…

One of the major challenges in machine learning nowadays is to provide predictions with not only high accuracy but also user-friendly explanations. Although in recent years we have witnessed increasingly popular use of deep neural networks…

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…

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…

State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study…

While state-of-the-art language models (LMs) surpass the vast majority of humans in certain domains, their reasoning remains largely opaque, undermining trust in their output. Furthermore, while autoregressive LMs can output explicit…

Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

Large language models (LLMs) have demonstrated impressive performance on natural language tasks, but their decision-making processes remain largely opaque. Existing explanation methods either suffer from limited faithfulness to the model's…

Prompt engineering has emerged as a powerful technique for guiding large language models (LLMs) toward desired responses, significantly enhancing their performance across diverse tasks. Beyond their role as static predictors, LLMs…

When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of…

Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems, for example, in Neural Theorem Provers (NTPs). These neuro-symbolic models can induce…

In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large…

LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic…

Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…

Large Language Models (LLMs) have shown significant promise in automated theorem proving, yet progress is often constrained by the scarcity of diverse and high-quality formal language data. To address this issue, we introduce…