Related papers: Epistemography and algebra
The constantly growing body of scholarly knowledge of science, technology, and humanities is an asset of the mankind. While new discoveries expand the existing knowledge, they may simultaneously render some of it obsolete. It is crucial for…
The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal…
Scientometrics is the study of the quantitative aspects of the process of science as a communication system. It is centrally, but not only, concerned with the analysis of citations in the academic literature. In recent years it has come to…
The paper investigates an evidence-based semantics for epistemic logics. It is shown that the properties of knowledge obtained from a potentially infinite body of evidence are described by modal logic S5. At the same time, the properties of…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
We introduce an approach to discovery informatics that uses so called knowledge graphs as the essential representation structure. Knowledge graph is an umbrella term that subsumes various approaches to tractable representation of large…
Research is described on a system for web-assisted education and how it is used to deliver on-line drill questions, automatically suited to individual students. The system can store and display all of the various pieces of information used…
Tables in scientific papers contain a wealth of valuable knowledge for the scientific enterprise. To help the many of us who frequently consult this type of knowledge, we present Tab2Know, a new end-to-end system to build a Knowledge Base…
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…
Social networks seeded, crystallized and structured by large-scale social platforms like Facebook, LinkedIn, Slack, Twitter, WhatsApp, Instagram and WeChat exhibit complicated epistemic structures and dynamics that arise from the nature of…
This paper presents a class of epistemic logics that captures the dynamics of acquiring knowledge and descending into oblivion, while incorporating concepts of group knowledge. The approach is grounded in a system of weighted models,…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Scholarly knowledge graphs are valuable sources of information in several research fields. Despite the number of existing datasets related to publications and researchers, resource quality, coverage and accessibility are still limited. This…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
A student's epistemological stance (be it knowledge as memorized information, knowledge from authority, or knowledge as invented stuff) may constrain that student from reasoning in productive ways while also shaping the inferences a…
We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…