Related papers: Simplifying Safety Proofs with Forward-Backward Re…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Inverse classification uses an induced classifier as a queryable oracle to guide test instances towards a preferred posterior class label. The result produced from the process is a set of instance-specific feature perturbations, or…
We present a novel proof by induction algorithm, which combines k-induction with invariants to model check C programs with bounded and unbounded loops. The k-induction algorithm consists of three cases: in the base case, we aim to find a…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…
The growing complexity of factual claims in real-world scenarios presents significant challenges for automated fact verification systems, particularly in accurately aggregating and reasoning over multi-hop evidence. Existing approaches…
Informal arguments that cryptographic protocols are secure can be made rigorous using inductive definitions. The approach is based on ordinary predicate calculus and copes with infinite-state systems. Proofs are generated using…
We consider concurrent systems consisting of a finite but unknown number of components, that are replicated instances of a given set of finite state automata. The components communicate by executing interactions which are simultaneous…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or…
We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal)…
The safety of automated driving systems must be justified by convincing arguments and supported by compelling evidence to persuade certification agencies, regulatory entities, and the general public to allow the systems on public roads.…
Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
An important problem in sequential decision-making under uncertainty is to use limited data to compute a safe policy, i.e., a policy that is guaranteed to perform at least as well as a given baseline strategy. In this paper, we develop and…
In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems. A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems. A numerical invariant of…