Related papers: Verifier Theory and Unverifiability
We present the Theorem Prover Museum, and initiative to conserve -- and make publicly available -- the sources and source-related artefacts of automated reasoning systems. Theorem provers have been at the forefront of Artificial…
We introduce the fundamental ideas and challenges of Predictable AI, a nascent research area that explores the ways in which we can anticipate key validity indicators (e.g., performance, safety) of present and future AI ecosystems. We argue…
The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and…
AI applications across classification, fairness, and human interaction often implicitly require ontologies of social concepts. Constructing these well, especially when there are many relevant categories, is a controversial task but is…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…
This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into…
We explore the following question: Is a decision-making program fair, for some useful definition of fairness? First, we describe how several algorithmic fairness questions can be phrased as program verification problems. Second, we discuss…
One of the greatest difficulties encountered by all in their first proof intensive class is subtly assuming an unproven fact in a proof. The purpose of this note is to describe a specific instance where this can occur, namely in results…
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
The search for a scientific theory of consciousness should result in theories that are falsifiable. However, here we show that falsification is especially problematic for theories of consciousness. We formally describe the standard…
The proliferation of Deep Neural Networks has resulted in machine learning systems becoming increasingly more present in various real-world applications. Consequently, there is a growing demand for highly reliable models in many domains,…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Interactive theorem proving software is typically designed around a trusted proof-checking kernel, the sole system component capable of authenticating theorems. Untrusted automation procedures reside outside of the kernel, and drive it to…
Classification may not be reliable for several reasons: noise in the data, insufficient input information, overlapping distributions and sharp definition of classes. Faced with several possibilities neural network may in such cases still be…
Earlier work on machine learning for automated reasoning mostly relied on simple, syntactic features combined with sophisticated learning techniques. Using ideas adopted in the software verification community, we propose the investigation…
A program verifier is a tool that can be used to verify that a "contract" for a program holds - i.e. given a precondition the program guarantees that a given postcondition holds - by only working at the level of the annotated program. An…
Artificial Knowledge (AK) systems are transforming decision-making across critical domains such as healthcare, finance, and criminal justice. However, their growing opacity presents governance challenges that current regulatory approaches,…