Related papers: Definitional Quantifiers Realise Semantic Reasonin…
Large Language Models (LLMs) have shown potential for solving mathematical tasks. We show that LLMs can be utilized to generate proofs by induction for hardware verification and thereby replace some of the manual work done by Formal…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
For over two decades Separation Logic has been arguably the most popular framework for reasoning about heap-manipulating programs, as well as reasoning about shared resources and permissions. Separation Logic is often extended to include…
We consider the problem of checking whether a proposed invariant $\varphi$ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
Continuous representations of logic formulae allow us to integrate symbolic knowledge into data-driven learning algorithms. If such embeddings are semantically consistent, i.e. if similar specifications are mapped into nearby vectors, they…
Most ATP benchmarks embed the final answer within the formal statement -- a convention we call "Easy Mode" -- a design that simplifies the task relative to what human competitors face and may lead to optimistic estimates of model…
Software verification of evolving systems is challenging mainstream methodologies and tools. Formal verification techniques often conflict with the time constraints imposed by change management practices for evolving systems. Since changes…
We present a trustworthy connection between the Leon verification system and the Isabelle proof assistant. Leon is a system for verifying functional Scala programs. It uses a variety of automated theorem provers (ATPs) to check verification…
Instruction following is a fundamental capability of large language models (LLMs), yet continuously improving this capability remains challenging. Existing methods typically rely either on costly external supervision from humans or strong…
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…
Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…
Teaching logic effectively requires an understanding of the factors which cause logic students to struggle. Formalization exercises, which require the student to produce a formula corresponding to the natural language sentence, are a good…
Our recently proposed certification framework for bit-level k-induction-based model checking has been shown to be quite effective in increasing the trust of verification results even though it partially involved quantifier reasoning. In…
Traditional program analysis analyses a program language, that is, all programs that can be written in the language. There is a difference, however, between all possible programs that can be written and the corpus of actual programs written…
We introduce DIVE, an end-to-end speaker diarization algorithm. Our neural algorithm presents the diarization task as an iterative process: it repeatedly builds a representation for each speaker before predicting the voice activity of each…
This paper presents rules of inference for a binary quantifier $I$ for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. $I$ binds one variable and forms a formula from two formulas.…
We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on…
The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…