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E-raamat: Geometry of Knowledge for Intelligent Systems

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Geometry of Knowledge for Intelligent SystemsSuurem pilt
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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.

Arvustused

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)

1 An Introduction to the Geometry of Agent Knowledge
1(4)
1.1 Introduction
1(4)
2 Tensor Calculus and Formal Concepts
5(26)
2.1 Vectors and Superposition of Attributes
5(9)
2.2 Invariants
14(17)
3 Geometry and Agent Coherence
31(30)
3.1 Agents and Coherence
33(5)
3.2 Field, Neural Network Geometry and Coherence
38(9)
3.3 Transformations in Which the General Quadratic Form Is Invariant
47(7)
3.3.1 Geometric Psychology and Coherence
50(4)
3.4 Local and Global Coherence Principle
54(7)
4 Field Theory for Knowledge
61(46)
4.1 Introduction
61(1)
4.2 Field of Conditional Probability and Tensor Image
61(5)
4.3 Geometry of Invariance and Symmetry in Population of Neurons by QMS (Quantum Morphogenetic System)
66(10)
4.3.1 Introduction
66(5)
4.3.2 Invariants and Symmetry
71(5)
4.4 Retina Model and Rotation Symmetry
76(6)
4.4.1 Sources and Transformations in Diffusion Reaction Equation
78(2)
4.4.2 Computational Experiments by Loo Chu Kiong [ ]
80(2)
4.4.3 Conclusion
82(1)
4.5 Quantum Mechanics and Non Euclidean Geometry
82(10)
4.5.1 Introduction
82(1)
4.5.2 Introduction to the Problem
82(1)
4.5.3 Hopfield Net and Quantum Holography by Morphogenetic System in Euclidean Geometry
83(4)
4.5.4 Hopfield Net and Quantum Holography by Morphogenetic System in Non Euclidean Geometry
87(3)
4.5.5 Computational Experiments by Professor Loo Chu Kiong
90(2)
4.5.6 Conclusions
92(1)
4.6 Superposition of Basis Field and Morphogenetic Field
92(10)
4.6.1 Objectives and Principles
93(3)
4.6.2 Example of Elementary Morphogenetic Field and Sources
96(2)
4.6.3 Example of DATA as Morphic Fields and Sources
98(2)
4.6.4 What Is Data Mining?
100(1)
4.6.5 Second Order Data Mining
101(1)
4.7 Example of Computation of Sources of Fields
102(5)
References
105(2)
5 Brain Neurodynamic and Tensor Calculus
107(52)
5.1 Properties and Geometry of Transformations Using Tensor Calculus
107(8)
5.2 Derivative Operator in Tensor Calculus and Commutators
115(8)
5.3 Neurodynamic and Tensor Space Image
123(1)
5.4 Introduction
123(1)
5.5 Constrains Description by States Manifold. [ 18]
124(1)
5.6 Metric Tensor and Geodesic in the Space of the States x
125(2)
5.7 Ordinary Differential Equation (ODE) in the Independent Variables by Geodesic
127(2)
5.8 Geodesic in Non Conservative Systems
129(2)
5.9 Amari [ 26] Information Space and Neurodynamic
131(2)
5.10 Electrical Circuit, Percolation and Geodesic [ 19]
133(2)
5.11 Neural Network Geodesic in the Space of the Electrical Currents [ 24][ 25]
135(1)
5.12 Toy Example of Geodesic and Electrical Circuit
135(10)
5.12.1 Membrane Electrical Activity and Geodesic
137(8)
5.13 Relation between Voltage Sources and Currents
145(1)
5.14 Geodesic in Presence of Voltage-Gated Channels in the Membrane
145(3)
5.15 Geodesic Image of the Synapses and Dendrites
148(3)
5.16 Geodesic Image of Shunting Inhibition
151(1)
5.17 Example of Implementation of Wanted Function in the CNS System
151(1)
5.18 Conclusion
152(7)
References
153(2)
Appendix A
155(4)
6 Electrical Circuit as Constrain in the Multidimensional Space of the Voltages or Currents
159(48)
6.1 Geometry of Voltage, Current, and Electrical Power
159(16)
6.1.1 Geometric Representation of the EC
163(5)
6.1.2 Electrical Power as Logistic Function in the Voltages m Dimensional Space
168(2)
6.1.3 Classical Parallel and Series Method to Compute Currents and Geometric Method
170(5)
6.2 A New Method to Compute the Inverse Matrix
175(10)
6.3 Electrical Circuit and the New Method for Inverse of the Matrix
185(6)
6.4 Transistor and Amplifier by Morphogenetic System
191(13)
6.5 Discussion
204(3)
References
205(2)
7 Superposition and Geometry for Evidence and Quantum Mechanics in the Tensor Calculus
207(22)
7.1 Introduction
207(1)
7.2 Evidence Theory and Geometry
207(2)
7.3 Geometric Interpretation of the Evidence Theory
209(9)
7.4 From Evidence Theory to Geometry
218(2)
7.5 Quantum Mechanics Interference and the Geometry of the Particles
220(8)
7.6 Conclusion
228(1)
References
228(1)
8 The Logic of Uncertainty and Geometry of the Worlds
229
8.1 Introduction
229(4)
8.2 Modal Logic and Meaning of Worlds
233(1)
8.3 Kripke Modal Framework
233(1)
8.4 Definitions of the Possible Worlds
234(1)
8.5 Meaning of the Possible World
235(2)
8.6 Discussion of Tarski's Truth Definition
237(3)
8.7 Possible World and Probability
240(2)
8.8 Break of Symmetry in Probability Calculus and Evidence Theory by Using Possible Worlds
242(7)
8.9 Fuzzy Set Theory
249(8)
8.9.1 Modified Probability Axioms Approach
249(3)
8.9.2 Fuzzy Logic Situations
252(5)
8.10 Context Space Approach
257(2)
8.11 Comparison of Two Approaches
259(1)
8.12 Irrational World or Agent
259(2)
8.13 Fuzzy Set, Zadeh Min Max Composition Rules and Irrationality
261(3)
8.14 Irrational and Rational Worlds
264(2)
8.15 Mapping Set of Worlds
266(2)
8.16 Invariant Expressions in Fuzzy Logic
268(1)
8.17 Linguistic Context Space of the Worlds
269(5)
8.18 Economic Model of Worlds
274(2)
8.19 Irrational Customers and Fuzzy Set
276(1)
8.20 Communication among Customers and Rough Sets
277(1)
8.21 Conclusion
278
References
278
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