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Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on…

Synthetic Separation Logic (SSL) is a formalism that powers SuSLik, the state-of-the-art approach for the deductive synthesis of provably-correct programs in C-like languages that manipulate Heap-based linked data structures. Despite its…

Inductive Logic Programming (ILP) provides interpretable rule learning in relational domains, yet remains limited in its ability to induce and reason with numerical constraints. Classical ILP systems operate over discrete predicates and…

Modern separation logics allow one to prove rich properties of intricate code, e.g. functional correctness and linearizability of non-blocking concurrent code. However, this expressiveness leads to a complexity that makes these logics…

Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…

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…

We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low…

Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…

Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL…

Linearisability has become the standard correctness criterion for concurrent data structures, ensuring that every history of invocations and responses of concurrent operations has a matching sequential history. Existing proofs of…

Language models (LMs) can perform complex reasoning either end-to-end, with hidden latent state, or compositionally, with transparent intermediate state. Composition offers benefits for interpretability and safety, but may need workflow…

Lighthouse projects such as CompCert, seL4, IronFleet, and DeepSpec have demonstrated that full verification of entire systems is feasible by establishing a refinement relation between an abstract system specification and an executable…

Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We…

Accurate uncertainty quantification is crucial for the safe deployment of machine learning models, and prior research has demonstrated improvements in the calibration of modern language models (LMs). We study in-context learning (ICL), a…

Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…

Bayesian probabilistic programming languages (BPPLs) let users denote statistical models as code while the interpreter infers the posterior distribution. The semantics of BPPLs are usually mathematically complex and unable to reason about…

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…

Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…

This paper develops a novel nested sequent proof-search methodology for intuitionistic tense logics (ITLs), supporting finite counter-model extraction. We introduce a new loop-checking method that detects repeating nested sequents using…

As a programming paradigm, answer set programming (ASP) brings about the usual issue of the human error. Hence, it is desirable to provide automated techniques that could help the programmer to find the error. This paper addresses the…