Related papers: Verifier Theory and Unverifiability
A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…
Software Model Checkers have shown outstanding performance improvements in recent times. Moreover, for specific use cases, formal verification techniques have shown to be highly effective, leading to a number of high-profile success…
Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks'…
The growing societal reliance on artificial intelligence necessitates robust frameworks for ensuring its security, accountability, and trustworthiness. This thesis addresses the complex interplay between privacy, verifiability, and…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
Deductive verification is an effective method to ensure that a given system exposes the intended behavior. In spite of its proven usefulness and feasibility in selected projects, deductive verification is still not a mainstream technique.…
We consider the problem of whether a given decision model, working with structured data, has individual fairness. Following the work of Dwork, a model is individually biased (or unfair) if there is a pair of valid inputs which are close to…
In parallel to the ever-growing usage of mechanized proofs in diverse areas of mathematics and computer science, proof assistants are used more and more for education. This paper surveys previous work related to the use of proof assistants…
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
Explainable AI (XAI) aims to address the human need for safe and reliable AI systems. However, numerous surveys emphasize the absence of a sound mathematical formalization of key XAI notions -- remarkably including the term "explanation"…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
How does the mathematical community accept that a given proof is correct? Is objective verification based on explicit axioms feasible, or must the reviewer's experiences and prejudices necessarily come into play? Can automated provers avoid…
There is a strong consensus that combining the versatility of machine learning with the assurances given by formal verification is highly desirable. It is much less clear what verified machine learning should mean exactly. We consider this…