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Human-machine networks affect many aspects of our lives: from sharing experiences with family and friends, knowledge creation and distance learning, and managing utility bills or providing feedback on retail items, to more specialised…
It is shown that a quantum computer can test the convexity and monotonicity of a given function exponentially more efficiently than a classical computer. This establishes another prominent example that showcases the potential of quantum…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
In high-stakes domains like healthcare, users often expect that sharing personal information with machine learning systems will yield tangible benefits, such as more accurate diagnoses and clearer explanations of contributing factors.…
Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.
Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…
The capabilities of large language models (LLMs) have raised concerns about their potential to create and propagate convincing narratives. Here, we study their performance in detecting convincing arguments to gain insights into LLMs'…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
The validity of online behavioral research relies on study participants being human rather than machine. In the past, it was possible to detect machines by posing simple challenges that were easily solved by humans but not by machines.…
Heterogeneity is a ubiquitous property of many biological systems and has profound implications for computation. While it is conceivable to optimize neuronal and synaptic heterogeneity for a specific task, such top-down optimization is…
Recent years have seen a boom in interest in machine learning systems that can provide a human-understandable rationale for their predictions or decisions. However, exactly what kinds of explanation are truly human-interpretable remains…
The article retraces major events and milestones in the mutual influences between mathematical logic and computer science since the 1950s.
We introduce a novel framework for incorporating human expertise into algorithmic predictions. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to predictive…
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory. While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms. In formal verification terms,…
Cooperation is often implicitly assumed when learning from other agents. Cooperation implies that the agent selecting the data, and the agent learning from the data, have the same goal, that the learner infer the intended hypothesis. Recent…
In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
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…
Machine learning is an important tool for decision making, but its ethical and responsible application requires rigorous vetting of its interpretability and utility: an understudied problem, particularly for natural language processing…