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LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main…
Proof by induction plays a critical role in formal verification and mathematics at large. However, its automation remains as one of the long-standing challenges in Computer Science. To address this problem, we developed sem_ind. Given…
Identifying the vulnerabilities of large language models (LLMs) is crucial for improving their safety by addressing inherent weaknesses. Jailbreaks, in which adversaries bypass safeguards with crafted input prompts, play a central role in…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
Formal verification is increasingly recognized as a critical foundation for building reliable software systems. However, the need for specialized expertise to write precise specifications, navigate complex proof obligations, and learn…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
METIS, the Mid-Infrared ELT Imager and Spectrograph, is one of the four first-generation ELT instruments scheduled to see first light in 2028. Its two main science modules are supported by an adaptive optics system featuring a pyramid…
The explainability of machine learning algorithms is crucial, and numerous methods have emerged recently. Local, post-hoc methods assign an attribution score to each feature, indicating its importance for the prediction. However, these…
Insertion Sequences (ISs) are small DNA segments that have the ability of moving themselves into genomes. These types of mobile genetic elements (MGEs) seem to play an essential role in genomes rearrangements and evolution of prokaryotic…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding…
Hallucination, the generation of factually incorrect content, is a growing challenge in Large Language Models (LLMs). Existing detection and mitigation methods are often isolated and insufficient for domain-specific needs, lacking a…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with limited computation power,…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
Using Isabelle/HOL, we verify the state-of-the-art decision procedure for multi-level syllogistic with singleton (MLSS for short), which is a quantifier-free fragment of set theory. We formalise its syntax and semantics as well as a sound…