Related papers: D-Hammer: Efficient Equational Reasoning for Label…
In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to…
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
Quantizers play a critical role in digital signal processing systems. Recent works have shown that the performance of quantization systems acquiring multiple analog signals using scalar analog-to-digital converters (ADCs) can be…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct…
Aligning large language models (LLMs) with a human reasoning approach ensures that LLMs produce morally correct and human-like decisions. Ethical concerns are raised because current models are prone to generating false positives and…
Inconsistencies are ubiquitous in law, administration, and jurisprudence. Though a cure is too much to hope for, we propose a technological remedy. Large language models (LLMs) can accurately extract propositions from arguments and compile…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
Neural methods have been shown to achieve high performance in Named Entity Recognition (NER), but rely on costly high-quality labeled data for training, which is not always available across languages. While previous works have shown that…
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns…
Academic and industrial sectors have been engaged in a fierce competition to develop quantum technologies, fueled by the explosive advancements in quantum hardware. While universal quantum computers have been shown to support up to hundreds…
We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…
What provides the highest level of assurance for correctness of execution within a programming language? One answer, and our solution in particular, to this problem is to provide a formalization for, if it exists, the denotational semantics…
Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving…
We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…
A first-order logic with quantum variables is needed as an assertion language for specifying and reasoning about various properties (e.g. correctness) of quantum programs. Surprisingly, such a logic is missing in the literature, and the…