Related papers: A Survey on Theorem Provers in Formal Methods
We investigate the reasons of having confidence in mathematical theorems. The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to this confidence. Opposing…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong…
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…
This study empirically validates automated logical specification methods for behavioural models, focusing on their robustness, scalability, and reproducibility. By the systematic reproduction and extension of prior results, we confirm key…
Despite recent advances in AI, the development of systems capable of executing complex, multi-step reasoning tasks involving multiple tools remains a significant challenge. Current benchmarks fall short in capturing the real-world…
The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…
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…
Proof engineering is notoriously labor-intensive: proofs that are straightforward on paper often require lengthy scripts in theorem provers. Recent advances in large language models (LLMs) create new opportunities for proof automation:…
Earlier work on machine learning for automated reasoning mostly relied on simple, syntactic features combined with sophisticated learning techniques. Using ideas adopted in the software verification community, we propose the investigation…
Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal…
We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem…
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…
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…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…