Related papers: Autoformalizing Euclidean Geometry
We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…
Large Language Models are increasingly used by students to explore advanced material in computer science, including graph theory. As these tools become integrated into undergraduate and graduate coursework, it is important to understand how…
Geometry problem solving has garnered increasing attention due to its potential applications in intelligent education field. Inspired by the observation that text often introduces ambiguities that diagrams can clarify, this paper presents…
Evaluating statement autoformalization, translating natural language mathematics into formal languages like Lean 4, remains a significant challenge, with few metrics, datasets, and standards to robustly measure progress. In this work, we…
We present a comprehensive approach to the automated formalization of legal texts using large language models (LLMs), targeting their transformation into Defeasible Deontic Logic (DDL). Our method employs a structured pipeline that segments…
Neurosymbolic approaches can add robustness to opaque neural systems by incorporating explainable symbolic representations. However, previous approaches have not used formal logic to contextualize queries to and validate outputs of large…
This study explores the use of Large Language Models (LLMs) for automatic evaluation of knowledge graph (KG) completion models. Historically, validating information in KGs has been a challenging task, requiring large-scale human annotation…
Recent advances in large language models (LLMs) have enabled the automatic generation of executable code for task planning and control in embodied agents such as robots, demonstrating the potential of LLM-based embodied intelligence.…
Humans, even at a very early age, can learn visual concepts and understand geometry and layout through active interaction with the environment, and generalize their compositions to complete tasks described by natural languages in novel…
Natural language explanations represent a proxy for evaluating explanation-based and multi-step Natural Language Inference (NLI) models. However, assessing the validity of explanations for NLI is challenging as it typically involves the…
The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most…
As LLM-based agents increasingly operate in high-stakes domains with real-world consequences, ensuring their behavioral safety becomes paramount. The dominant oversight paradigm, LLM-as-a-Judge, faces a fundamental dilemma: how can…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
Large language models (LLMs) are trained and tested extensively on symbolic representations such as code and graphs, yet real-world user tasks are often specified in natural language. To what extent can LLMs generalize across these…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
Unlabeled LiDAR logs, in autonomous driving applications, are inherently a gold mine of dense 3D geometry hiding in plain sight - yet they are almost useless without human labels, highlighting a dominant cost barrier for…
The Unified Modelling Language is emerging as a de-facto standard for modelling object-oriented systems. However, the semantics document that a part of the standard definition primarily provides a description of the language's syntax and…
AutomationML (AML) enables standardized data exchange in engineering, yet existing recommendations for proper AML modeling are typically formulated as informal and textual constraints. These constraints cannot be validated automatically…
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…