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2013 | Book

An Introduction to the Geometry of Agent Knowledge Read chapter Read first chapter

Geometry of Knowledge for Intelligent Systems

Author: Germano Resconi

Publisher: Springer Berlin Heidelberg

Book Series : Studies in Computational Intelligence

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

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.

Table of Contents

Frontmatter
An Introduction to the Geometry of Agent Knowledge
Abstract
This chapter provides an introduction to the geometry of knowledge. It briefly introduces important concepts and presents a summary of the contents of the book.
Germano Resconi
Tensor Calculus and Formal Concepts
Abstract
This chapter introduces tensor calculus using formal concepts which aid the better understanding of intelligence.
Germano Resconi
Geometry and Agent Coherence
Abstract
This chapter presents the geometric coherence of the agent expressed by a graph of actions (flow) and nodes that can be sources or tasks (effort). Any graph source, action, tasks. Any agent of the first order can be considered to be a system, which by the use of resources can activate an action, which enables the task to be done. Resources can be physical resources, functions, tables of data or any type of information necessary to do the action. Action is a method or a set of methods by which we solve our problem. Initially, we can represent any simple agent using figure 3.1 and a network of simple agents.
Germano Resconi
Field Theory for Knowledge
Introduction
In this chapter we show the spectrum of the possible field of research of the non Euclidean geometry and morphogenetic fields. The Green function extensively used in the solution of linear differential equation assumes a new geometric image and is extended beyond the traditional field of differential equations.
Germano Resconi
Brain Neurodynamic and Tensor Calculus
Abstract
This chapter presents the neurodynamic of brain as a part of a geometric space. Logic is not only true and false but new topics in logic as fuzzy set and many valued logic extend the simple idea of true and false to values or coordinates in geometric space where the true and false are positions in this space. Thus, the holistic approach to Fuzzy and many value logic of the agent can be well represented by geometry of agent knowledge. We assume that Logic is included into the neurodynamic of the Brain.
Germano Resconi
Electrical Circuit as Constrain in the Multidimensional Space of the Voltages or Currents
Abstract
In this chapter we will show that electrical circuit can be represented as a projection of a vector in the voltage space into a subspace where defined constrain is satisfy. Let us consider the electrical circuit shown in figure 6.1 where ek are the edges of the circuit, V are the electrical potentials in the nodes, Zk are the impedances and ik are the currents.
Germano Resconi
Superposition and Geometry for Evidence and Quantum Mechanics in the Tensor Calculus
Introduction
In this chapter we prove that the interference in Coherent Quantum Mechanics is represented by a deformed space of the intensity for different particle beams. In the interference the complex number representation of the quantum mechanics is substituted by general real coordinates where the angles between general coordinates are the difference of the phases. To reformulate the traditional quantum model, we use the evidence theory and its geometric image. The evidence theory defines a non additive probability denoted basic probability assignment. We assume that in quantum mechanics for interference and entanglement phenomena, the probability is not the traditional probability but is the basic probability assignment in the evidence theory.
Germano Resconi
The Logic of Uncertainty and Geometry of the Worlds
Abstract
The classical logic is built in an axiomatic way without containing any uncertainty. Over the years, many attempts have been made to extend the classical logic framework to incorporate uncertainties. This work has produced different and apparently conflicting definitions of uncertainties. Previously we have argued that an extended modal logic framework can provide a unifying formal language for many formalizations of uncertainty such as probability, approximate probability, evidence theory, fuzzy sets, and rough sets.
In this chapter, we have shown how such an extended modal of logic framework provides a unifying formal language for formalizations of probability and fuzzy sets theories. We also show that this originally pure theoretical approach can be used to describe a mathematical model for linguistic uncertainty in a unified framework. The approach combines concepts of modal logic together the linguistic context space previously proposed. This combined approach is illustrated with an application to the question of economical preference between customers and goods.
A common language able to represent different types of uncertainties is useful because it allows us to define the uncertainties using simple entities and to compare different types of uncertainties as being different aspects of the same fundamental structure. The justification of different theories of uncertainty using a unified language is beyond the scope of this paper.
Our goal is to rebuild a foundation of the uncertainty concept by using a new interpretation of the modal logic structure. Using this new foundation we discover that disparate types of uncertainties and the idea of uncertainty itself can be understood. This new foundation opens opportunities to discover hidden connection between different types of uncertainties.
Germano Resconi
Metadata
Title
Geometry of Knowledge for Intelligent Systems
Author
Germano Resconi
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-27972-0
Print ISBN
978-3-642-27971-3
DOI
https://doi.org/10.1007/978-3-642-27972-0

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