相关论文: Implicit and Explicit Proof Management in KeYmaera…
The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…
We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…
Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al.,…
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information…
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…
Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…
It is explored that available credible evidence fusion schemes suffer from the potential inconsistency because credibility calculation and Dempster's combination rule-based fusion are sequentially performed in an open-loop style. This paper…
Recent work by Clark et al. (2020) shows that transformers can act as 'soft theorem provers' by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
The analyzability of hybrid software, which integrates both classical and quantum components, is a key factor in ensuring its maintainability and industrial adoption. This article presents the empirical validation, through a family of…
We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the…
The complexity of modern software systems entails the need for reconfiguration mechanisms gov- erning the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally,…
We present three contributions to the understanding of QMA with multiple provers: 1) We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap Omega(1/N^2). Our improvement is achieved…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…