Geometry of Knowledge for Intelligent Systems

1. Front Matter

   Pages 1-7

   PDF

2. An Introduction to the Geometry of Agent Knowledge

   • Germano Resconi

   Pages 1-3

3. Tensor Calculus and Formal Concepts

   • Germano Resconi

   Pages 5-29

4. Geometry and Agent Coherence

   • Germano Resconi

   Pages 31-60

5. Field Theory for Knowledge

   • Germano Resconi

   Pages 61-105

6. Brain Neurodynamic and Tensor Calculus

   • Germano Resconi

   Pages 107-158

7. Electrical Circuit as Constrain in the Multidimensional Space of the Voltages or Currents

   • Germano Resconi

   Pages 159-206

8. Superposition and Geometry for Evidence and Quantum Mechanics in the Tensor Calculus

   • Germano Resconi

   Pages 207-228

9. The Logic of Uncertainty and Geometry of the Worlds

   • Germano Resconi

   Pages 229-279

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.

• Computational Intelligence
• Intelligent Systems
• Uncertainty

From the reviews:

“The book puts forward a bridge between agent-based systems and tensor calculus, presenting agent knowledge in a geometric way. … all the modern topics for modeling agent-based systems, like data mining, neural networks, fuzzy and many value logic, are brought together through a geometric reference. The book will be especially valued by those researchers that, beyond computer science, mathematics or physics, express as well interest in philosophy.” (Ruxandra Stoean, Zentralblatt MATH, Vol. 1260, 2013)

• Dept. Mathematics and Physics, Catholic University, Brescia, Italy

  Germano Resconi

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