Geometry of Knowledge for Intelligent Systems - Resconi, Germano; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013)
The book is on the geometry of agent knowledge. The important concept studied in this book is the Field and its Geometric Representation. To develop a geometric image of the gravity , Einstein used Tensor Calculus but this is very different from the knowledge instruments used now, as for instance techniques of data mining , neural networks , formal concept analysis ,quantum computer and other topics. The aim of this book is to rebuild the tensor calculus in order to give a geometric representation of agent knowledge. By using a new geometry of knowledge we can unify all the topics that have been studied in recent years to create a bridge between the geometric representation of the physical phenomena and the geometric representation of the individual and subjective knowledge of the agents.
An Introduction to the Geometry of Agent Knowledge -- Tensor Calculus and Formal Concepts -- Geometry and Agent Coherence -- Field Theory for Knowledge -- Brain Neurodynamic and Tensor Calculus -- Electrical Circuit as constrain in the multidimensional space of the voltages or currents -- Superposition and Geometry for Evidence and Quantum Mechanics in the Tensor Calculus -- The Logic of Uncertainty and geometry of the worlds.
Keywords: Engineering; Artificial intelligence; Mathematics; Engineering mathematics; Engineering; Appl.Mathematics/Computational Methods of Engineering; Artificial Intelligence (incl. Robotics).; Applications of Mathematics