Related papers: Certified $\Sigma_1$-sentences
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…
This vision paper articulates a long-term research agenda for formal methods at the intersection with artificial intelligence, outlining multiple conceptual and technical dimensions and reporting on our ongoing work toward realising this…
Verifiable generation requires large language models (LLMs) to cite source documents supporting their outputs, thereby improve output transparency and trustworthiness. Yet, previous work mainly targets the generation of sentence-level…
Proving the efficacy of certification standards
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with…
Certifying verification algorithms not only return whether a given property holds or not, but also provide an accompanying independently checkable certificate and a corresponding witness. The certificate can be used to easily validate the…
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…
CeTA was originally developed as a tool for certifying termination proofs which have to be provided as certificates in the CPF-format. Its soundness is proven as part of IsaFoR, the Isabelle Formalization of Rewriting. By now, CeTA can also…
Evidence plays a crucial role in automated fact-checking. When verifying real-world claims, existing fact-checking systems either assume the evidence sentences are given or use the search snippets returned by the search engine. Such methods…
We provide a wide-ranging study of the scenario where a subset of the relations in a relational vocabulary are visible to a user --- that is, their complete contents are known --- while the remaining relations are invisible. We also have a…
Checking and confirming factual information in texts and speeches is vital to determine the veracity and correctness of the factual statements. This work was previously done by journalists and other manual means but it is a time-consuming…
A wide range of learning tasks require human input in labeling massive data. The collected data though are usually low quality and contain inaccuracies and errors. As a result, modern science and business face the problem of learning from…
We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using $\sigma$-algebras, we define what a proof of a number-theoretical statement by Language Theory means. We prove…
Proposition. Let $f$ be a predictor trained on a distribution $P$ and evaluated on a shifted distribution $Q$. Under verifiable regularity and complexity constraints, the excess risk under shift admits an explicit upper bound determined by…
Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any L_F-sentence \varphi containing only bounded quantifiers, and any positive rational number \delta, decides either "\varphi…
We investigate the trade-off between certificate length and verifier runtime. We prove a Verifier Trade-off Theorem showing that reducing the inherent verification time of a language from \(f(n)\) to \(g(n)\), where \(f(n) \ge g(n)\),…
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…
The literature on provable robustness in machine learning has primarily focused on static prediction problems, such as image classification, in which input samples are assumed to be independent and model performance is measured as an…
We consider the signatures $\Sigma_m=(0,1,-,+, \cdot, \ ^{-1})$ of meadows and $(\Sigma_m, {\mathbf s})$ of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these…