The Spaces of Data, Information, and Knowledge
Xiaoyu Chen, Dongming Wang

TL;DR
This paper develops a topological framework for understanding data, information, and knowledge spaces, highlighting how data interpretation, relation generalization, and validation processes enable automatic discovery of profound knowledge, exemplified in geometry.
Contribution
It introduces a formal topological model of data, information, and knowledge spaces, clarifying the processes of data interpretation, relation induction, and validation for automatic knowledge discovery.
Findings
Data interpretation and relation mining are key to information retrieval.
Induction and deduction principles facilitate knowledge generation.
The framework is demonstrated through a geometry case study.
Abstract
We study the data space of any given data set and explain how functions and relations are defined over . From and for a specific domain we construct the information space of by interpreting variables, functions, and explicit relations over in and by including other relations that implies under the interpretation in . Then from we build up the knowledge space of as the product of two spaces and , where is obtained from by using the induction principle to generalize propositional relations to quantified relations, the deduction principle to generate new relations, and standard mechanisms to validate relations and is the space of specifications of methods with operational instructions which are valid in . Through our construction of the three topological spaces the following key observation…
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Taxonomy
TopicsTopological and Geometric Data Analysis · Data Management and Algorithms · Rough Sets and Fuzzy Logic
