Vector Analysis of Problem Spaces Based on Human-Machine Interaction

ABSTRACT

As a problem, space is the implicit world of cognition, it is difficult to observe and collect its data. From the new perspective of cognitive philosophy, human-machine cognitive coupling is the coupled state of the intelligent agent and the information system. The extension of a problem space inside the brain makes observation possible. The data for a problem space constitutes a set and forms a tree topology according to the level of cognitive abstraction. On the basis of mathematical paradigms, the metric specifications of problems are built on problem topology. Vector analysis is carried out on the problem space. The size, direction, hierarchy, and vector addition and subtraction of objects of a problem space are defined. On the basis of topological dynamic theory, the topological dynamic orbit of a problem space is defined. The topological reconstruction and vector analysis of problem spaces provides new methods for the refined detection of the structure of problem spaces.

Keywords:

Cognitive dynamics system, E-learning, Human-machine interaction, Problem space, Topological manifold.