Related papers: Mathematics, Recursion, and Universals in Human La…
We investigate mechanisms for language change within a framework where an unconventional signal for a meaning is first innovated, and then subsequently propagated through a speech community to replace the existing convention. We appeal to…
Language technologies that accurately model the dynamics of events must perform commonsense reasoning. Existing work evaluating commonsense reasoning focuses on making inferences about common, everyday situations. To instead investigate the…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…
The outline of a programme for restructuring mathematical logic. We explain what we mean by "restructuring" and carry out exemplary parts of the programme.
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
Mathematicians invented Mathematics to escape from words, but at last they depend on them just as much as everybody else. At the end, all basic definitions will be reliant on words, yet the mathematician believes that he's elevated from…
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
This book invites readers to see mathematics not just as formulas and rules, but as the deepest expression of human thought. It begins by exploring the timeless idea of mathematics as a universal language, contrasting its precision with the…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
Matrix syntax is a formal model of syntactic relations in language. The purpose of this paper is to explain its mathematical foundations, for an audience with some formal background. We make an axiomatic presentation, motivating each axiom…
The use of terms from natural and social scientific titles and abstracts is studied from the perspective of sublanguages and their specialized dictionaries. Different notions of sublanguage distinctiveness are explored. Objective methods…
The application of physics formulas is a fundamental human capability in numerical reasoning. While existing datasets often rely on implicit mathematical knowledge, they rarely explicitate the underlying formulas. To address this, we…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
"Natural Language," whether spoken and attended to by humans, or processed and generated by computers, requires networked structures that reflect creative processes in semantic, syntactic, phonetic, linguistic, social, emotional, and…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…