Related papers: Parmesan: mathematical concept extraction for educ…
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from G\"ardenfors semantic spaces, categorical compositional linguistics, and…
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…
This paper describes how automated deduction methods for natural language processing can be applied more efficiently by encoding context in a more elaborate way. Our work is based on formal approaches to context, and we provide a tableau…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
Natural Language Processing (NLP) aims to analyze text or speech via techniques in the computer science field. It serves applications in the domains of healthcare, commerce, education, and so on. Particularly, NLP has been widely applied to…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…
In natural-language discourse, related events tend to appear near each other to describe a larger scenario. Such structures can be formalized by the notion of a frame (a.k.a. template), which comprises a set of related events and…
It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making…
Advances in large language models (LLMs) have spurred research into enhancing their reasoning capabilities, particularly in math-rich STEM (Science, Technology, Engineering, and Mathematics) documents. While LLMs can generate equations or…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
In this article we consider the basic ideas, approaches and results of developing of mathematical knowledge management technologies based on ontologies. These solutions form the basis of a specialized digital ecosystem OntoMath which…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
Statistical topic models provide a general data-driven framework for automated discovery of high-level knowledge from large collections of text documents. While topic models can potentially discover a broad range of themes in a data set,…
This paper presents a computational model of concept learning using Bayesian inference for a grammatically structured hypothesis space, and test the model on multisensory (visual and haptics) recognition of 3D objects. The study is…
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to…
This paper is devoted to the problems of ontology-based mathematical knowledge management and representation. The main attention is paid to the development of a formal model for the representation of mathematical statements in the Open…
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism…
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…
General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might…