Related papers: Epistemography and algebra
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
This paper combines the classical model of labeled transition systems with the epistemic model for reasoning about knowledge. The result is a unifying framework for modeling and analyzing multi-agent, knowledge-based, dynamic systems. On…
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this…
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…
Several technologies are emerging that provide new ways to capture, store, present and use knowledge. This book is the first to provide a comprehensive introduction to five of the most important of these technologies: Knowledge Engineering,…
We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the…
We define a notion of social machine and envisage an algebra that can describe networks of such. To start with, social machines are defined as tuples of input, output, processes, constraints, state, requests and responses; apart from…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…
The notion of argumentation and the one of belief stand in a problematic relation to one another. On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably)…
The application of mathematics and statistical methods to scholarly communication: scientometrics, has facilitated the systematic analysis of the modern digital tide of literature. This chapter reviews three of such applications:…
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
Organized knowledge production can then be considered as the codification of communication. Communications leave traces that can be studied as indicators. Institutions can be considered as retention mechanisms functional for the…
The existence of a coalition strategy to achieve a goal does not necessarily mean that the coalition has enough information to know how to follow the strategy. Neither does it mean that the coalition knows that such a strategy exists. The…
Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real solutions to such systems, particularly…
The trends of open science have enabled several open scholarly datasets which include millions of papers and authors. Managing, exploring, and utilizing such large and complicated datasets effectively are challenging. In recent years, the…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
When presented with information of any type, from music to language to mathematics, the human mind subconsciously arranges it into a network. A network puts pieces of information like musical notes, syllables or mathematical concepts into…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…