Introduction to the mathematical theory of knowledge conceptualization: Conceptual systems and structures

Abstract

The paper departs from the general problem of knowledge integration and the basic strategies that can be adopted to confront this challenge. With the purpose of providing a sound meta-theoretical framework to facilitate knowledge conceptualization and integration, as well as assessment criteria to evaluate achievements regarding knowledge integration, the paper first reviews the previous work in the field of conceptual spaces. It subsequently gives an overview of structural tools and mechanisms for knowledge representation, recapped in the modal stratified bond model of global knowledge. On these groundings, a novel formalized representation of conceptual systems, structures, spaces and algebras is developed through a set of definitions which goes beyond the exploration of mental knowledge representation and the semantics of natural languages. These two components provide a sound framework for the development of the glossaLAB international project with respect to its two basic objectives, namely (i) facilitating knowledge integration in general and particularly in the context of the general study of information and systems; (ii) facilitating the assessment of the achievements as regards knowledge integration in interdisciplinary settings. An additional article tackles the solutions adopted to integrate these results in the elucidation of the conceptual network of the general study of information and systems.