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Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…
We report on our journey to develop ProofBuddy, a web application that is powered by a server-side instance of the proof assistant Isabelle, for the teaching and learning of proofs and proving. The journey started from an attempt to use…
The exploration \& exploitation dilemma poses significant challenges in reinforcement learning (RL). Recently, curiosity-based exploration methods achieved great success in tackling hard-exploration problems. However, they necessitate…
The motivation of this study is to leverage recent breakthroughs in artificial intelligence research to unlock novel solutions to important scientific problems encountered in computational science. To address the human intelligence…
Automated penetration testing (AutoPT) powered by large language models (LLMs) has gained attention for its ability to automate ethical hacking processes and identify vulnerabilities in target systems by leveraging the inherent knowledge of…
Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These…
Hierarchical factor models, which include the bifactor model as a special case, are useful in social and behavioural sciences for measuring hierarchically structured constructs. Specifying a hierarchical factor model involves imposing…
We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
In successful enterprise attacks, adversaries often need to gain access to additional machines beyond their initial point of compromise, a set of internal movements known as lateral movement. We present Hopper, a system for detecting…
Multi-agent reinforcement learning has received significant interest in recent years notably due to the advancements made in deep reinforcement learning which have allowed for the developments of new architectures and learning algorithms.…
This paper attempts to address the question of how best to assure the correctness of saturation-based automated theorem provers using our experience developing the theorem prover Vampire. We describe the techniques we currently employ to…
Large language models (LLMs) have enabled agentic AI systems for scientific discovery, but most approaches remain limited to textbased reasoning without automated experimental verification. We propose MIND, an LLM-driven framework for…
We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with…
We describe Imandra, a modern computational logic theorem prover designed to bridge the gap between decision procedures such as SMT, semi-automatic inductive provers of the Boyer-Moore family like ACL2, and interactive proof assistants for…
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…
We describe an inductive logic programming (ILP) approach called learning from failures. In this approach, an ILP system (the learner) decomposes the learning problem into three separate stages: generate, test, and constrain. In the…
The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand…