Related papers: Verifier Theory and Unverifiability
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
This report describes the state of the art in verifiable computation. The problem being solved is the following: The Verifiable Computation Problem (Verifiable Computing Problem) Suppose we have two computing agents. The first agent is the…
In recent years, program verifiers and interactive theorem provers have become more powerful and more suitable for verifying large programs or proofs. This has demonstrated the need for improving the user experience of these tools to…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
Model checkers use automated state exploration in order to prove various properties such as reachability, non-reachability, and bisimulation over state transition systems. While model checkers have proved valuable for locating errors in…
Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security,…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
Proof scores can be regarded as outlines of the formal verification of system properties. They have been historically used by the OBJ family of specification languages. The main advantage of proof scores is that they follow the same syntax…
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
For AI systems to garner widespread public acceptance, we must develop methods capable of explaining the decisions of black-box models such as neural networks. In this work, we identify two issues of current explanatory methods. First, we…
The current literature on AI-advised decision making -- involving explainable AI systems advising human decision makers -- presents a series of inconclusive and confounding results. To synthesize these findings, we propose a simple theory…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…
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…
Transformers have had a significant impact on natural language processing and have recently demonstrated their potential in computer vision. They have shown promising results over convolution neural networks in fundamental computer vision…
In the last decades, several objects such as grammars, economical agents, laws of physics... have been defined as algorithms. In particular, after Brouwer, Heyting, and Kolomogorov, mathematical proofs have been defined as algorithms. In…
This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its…
We analyze the informal semantic conception of proof and axiomatize the proof relation and the provability operator. A self referential propositional calculus which admits provable liar type sentences is introduced and proven consistent. We…