Related papers: ProofPeer: Collaborative Theorem Proving
Textual content is often the output of a collaborative writing process: We start with an initial draft, ask for suggestions, and repeatedly make changes. Agnostic of this process, today's language models are trained to generate only the…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
Formal verification of neuro-symbolic cyber-physical systems, such as drones, medical devices and robots, is complicated. Neural components must be trained to be optimal with respect to the available data as well as the safety…
We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear…
Commonsense fact verification, as a challenging branch of commonsense question-answering (QA), aims to verify through facts whether a given commonsense claim is correct or not. Answering commonsense questions necessitates a combination of…
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…
The paper gives a detailed presentation of a framework, embedded into the simply typed higher-order logic and aimed at the support of sound and structured reasoning about various properties of models of imperative programs with interleaved…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context. This is based on my talk at the PQR conference (Brussels, June 2003).
Much of machine learning research focuses on predictive accuracy: given a task, create a machine learning model (or algorithm) that maximizes accuracy. In many settings, however, the final prediction or decision of a system is under the…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
Suppose we need a deep collective analysis of an open scientific problem: there is a complex scientific hypothesis and a large online group of mutually unrelated experts with relevant private information of a diverse and unpredictable…
Collaboration in multi-agent autonomous systems is critical to increase performance while ensuring safety. However, due to heterogeneity of their features in, e.g., perception qualities, some autonomous systems have to be considered more…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
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…
Recent progress in formal theorem proving has benefited from large-scale proof generation and verifier-aware training, but agentic proving is rarely integrated into prover training, appearing only at inference time. We present OProver, a…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…