Related papers: $\alpha$Check: A mechanized metatheory model-check…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
Software model checking, as an undecidable problem, has three possible outcomes: (1) the program satisfies the specification, (2) the program does not satisfy the specification, and (3) the model checker fails. The third outcome usually…
The demand for formal verification tools for neural networks has increased as neural networks have been deployed in a growing number of safety-critical applications. Matrices are a data structure essential to formalising neural networks.…
In data analysis, unexpected results often prompt researchers to revisit their procedures to identify potential issues. While some researchers may struggle to identify the root causes, experienced researchers can often quickly diagnose…
Conformance checking is a set of process mining functions that compare process instances with a given process model. It identifies deviations between the process instances' actual behaviour ("as-is") and its modelled behaviour ("to-be").…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
We consider the problem of the verification of an LTL specification $\varphi$ on a system $S$ given some prior knowledge $K$, an LTL formula that $S$ is known to satisfy. The automata-theoretic approach to LTL model checking is implemented…
This paper presents the first model-checking algorithm for an expressive modal mu-calculus over timed automata, $L^{\mathit{rel}, \mathit{af}}_{\nu,\mu}$, and reports performance results for an implementation. This mu-calculus contains…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
Model checking invariant properties of designs, represented as transition systems, with non-linear real arithmetic (NRA), is an important though very hard problem. On the one hand NRA is a hard-to-solve theory; on the other hand most of the…
The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself -- or its implementation -- is not formally checked. We address this…
Large Language Models have significantly advanced natural language processing tasks, but remain prone to generating incorrect or misleading but plausible arguments. This issue, known as hallucination, is particularly concerning in…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
These notes present some extensions of a formal method introduced in an earlier paper. The formal method is designed as a tool for program verification of numerical computation and forms the basis of the software package VPC. Included in…
Minimax-based search algorithms with alpha-beta pruning and transposition tables are a central component of classical game-playing engines and remain widely used in practice. Despite their widespread use, these algorithms are subtle, highly…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
Automatic fake news detection models are ostensibly based on logic, where the truth of a claim made in a headline can be determined by supporting or refuting evidence found in a resulting web query. These models are believed to be reasoning…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Even competent programmers make mistakes. Automatic verification can detect errors, but leaves the frustrating task of finding the erroneous line of code to the user. This paper presents an automatic approach for identifying potential error…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…