Related papers: A general proof certification framework for modal …
We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language…
While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains an open problem for model interpretability. We propose a novel theoretical lens for…
In the last decade, a large body of work has emerged on robustness of neural networks, i.e., checking if the decision remains unchanged when the input is slightly perturbed. However, most of these approaches ignore the confidence of a…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Programming language frameworks allow us to generate language tools (e.g., interpreters) just from a formal description of the syntax and semantics of a programming language. As these frameworks tend to be quite complex, an issue arises…
In this paper, we prove correctness of parallelizing a string matcher using Haskell as a theorem prover. We use refinement types to specify correctness properties, Haskell terms to express proofs and Liquid Haskell to check correctness of…
The certification of autonomous systems is an important concern in science and industry. The KI-LOK project explores new methods for certifying and safely integrating AI components into autonomous trains. We pursued a two-layered approach:…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
Number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects…
Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on…
We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological…
We introduce Goedel-Prover, an open-source language model that achieves state-of-the-art (as of April 5 2025) performance in automated formal proof generation for mathematical problems. A key challenge in this field is the scarcity of…
The free-variable tableau method has been widely used in order to automate proofs in multiple kinds of logics. Many automated theorem provers rely on this approach, either because it is the only available method-e.g., in certain modal…
The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself -- or its implementation -- is not formally checked. We address this…
Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely…
We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…