Related papers: Verifier Theory and Unverifiability
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Explainable AI has become a common term in the literature, scrutinized by computer scientists and statisticians and highlighted by psychological or philosophical researchers. One major effort many researchers tackle is constructing general…
There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…
Explainability has been an important goal since the early days of Artificial Intelligence. Several approaches for producing explanations have been developed. However, many of these approaches were tightly coupled with the capabilities of…
Verified artificial intelligence (AI) is the goal of designing AI-based systems that that have strong, ideally provable, assurances of correctness with respect to mathematically-specified requirements. This paper considers Verified AI from…
Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
Neural network models trained on text data have been found to encode undesirable linguistic or sensitive concepts in their representation. Removing such concepts is non-trivial because of a complex relationship between the concept, text…
Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN…
Universal quantifiers occur frequently in proof obligations produced by program verifiers, for instance, to axiomatize uninterpreted functions and to express properties of arrays. SMT-based verifiers typically reason about them via…
Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…
Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the…
Reproducibility is one of the core dimensions that concur to deliver Trustworthy Artificial Intelligence. Broadly speaking, reproducibility can be defined as the possibility to reproduce the same or a similar experiment or method, thereby…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
This dissertation discusses several problems loosely related, because they all involve a verification condition generator. The Boogie language is introduced; the architecture of a verification-generator is described. Then come more…
Verifiers are crucial components for enhancing modern LLMs' reasoning capability. Typicalverifiers require resource-intensive superviseddataset construction, which is costly and faceslimitations in data diversity. In this paper, wepropose…
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
This paper deals with belief base revision that is a form of belief change consisting of the incorporation of new facts into an agent's beliefs represented by a finite set of propositional formulas. In the aim to guarantee more reliability…
Large language models (LLMs) can act as both problem solvers and solution verifiers, where the latter select high-quality answers from a pool of solver-generated candidates. This raises the question of under what conditions verification…
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…