Related papers: Accepted proofs: Objective truth, or culturally ro…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
A successful automated program proof is, in software verification, the ultimate triumph. In practice, however, the road to such success is paved with many failed proof attempts. Unlike a failed test, which provides concrete evidence of an…
The analysis of the adaptive behaviour of many different kinds of systems such as humans, animals and machines, requires more general ways of assessing their cognitive abilities. This need is strengthened by increasingly more tasks being…
We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to…
While recent years have witnessed the emergence of various explainable methods in machine learning, to what degree the explanations really represent the reasoning process behind the model prediction -- namely, the faithfulness of…
Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…
We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability…
Formal verification of software is a bit of a niche activity: it is only applied to the most safety-critical or security-critical software and it is typically only performed by specialized verification engineers. This paper considers…
Despite significant progress, evaluation of explainable artificial intelligence remains elusive and challenging. In this paper we propose a fine-grained validation framework that is not overly reliant on any one facet of these…
Code metrics are easy to define, but not so easy to justify. It is hard to prove that a metric is valid, i.e., that measured numerical values imply anything on the vaguely defined, yet crucial software properties such as complexity and…
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…
Crises in peer review capacity, study replication, and AI-fabricated science have intensified interest in automated tools for assessing scientific research. However, the scientific community has a history of decontextualizing and…
Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
Artificial Intelligence (AI) provides many opportunities to improve private and public life. Discovering patterns and structures in large troves of data in an automated manner is a core component of data science, and currently drives…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…