Boolean Structures: Combinatorics, Codification, Representation

Contents
List of Tables
List of Figures
1. Introduction
	1.1. Logic is the Only Self–grounding Knowledge
	1.2. Is Logic Arbitrary?
	1.3. The Issue of Quantification
	1.4. Traditional Approach to Boolean Algebra
	1.5. About the Notation
2. Preliminary Notions
	2.1. Basic Operations
	2.2. Sets and Classes
	2.3. Basic Numbers
	2.4. First Examples of Algebra
	2.5. Algebraic Computation
3. B3
	3.1. General Considerations
		3.1.1. Main code alphabets
		3.1.2. Subcode alphabets
		3.1.3. Transformation rules
	3.2. Different Levels
		3.2.1. From Level 1/8 to Level 2/8
		3.2.2. From Level 2/8 to Level 3/8
		3.2.3. From Level 3/8 to Level 4/8
		3.2.4. From Level 4/8 to Level 5/8
		3.2.5. From Level 5/8 to Level 6/8
		3.2.6. From Level 6/8 to Level 7/8
		3.2.7. Summary
	3.3. Distribution
	3.4. Other Cases
		3.4.1. Reduction of other algebras to complete algebras
		3.4.2. A closer look to 6 digits
		3.4.3. Anomalous sets and subsets
4. B4
	4.1. Self–dual Variables
	4.2. SCAs
	4.3. Some Examples of Nodes
		4.3.1. 2–chunks
		4.3.2. Levels 2/16 and 3/16
		4.3.3. Levels 4/16 and 5/16
		4.3.4. Levels 6/16 and 7/16
		4.3.5. Level 8/16
		4.3.6. Summary of the following levels
	4.4. Generalisations
		4.4.1. Combinatorics of nodes
		4.4.2. Summary of the logical forms
5. B5
	5.1. SD Variables and CAs
	5.2. SCAs
	5.3. Examples of Nodes
6. Codification
	6.1. Codification in General
	6.2. Colour Codification
	6.3. The Genetic Code
	6.4. Classifying Things and Data
		6.4.1. Basic classifications
		6.4.2. Hierarchies
		6.4.3. Playing with networks
		6.4.4. Properties
		6.4.5. Individuals
		6.4.6. Some additional words
7. Logical Spaces and Quantum Information
	7.1. From IDs to Vectors
	7.2. Practical Representation
	7.3. Quantum Networks
		7.3.1. Superposition state
		7.3.2. Bell states
		7.3.3. A worry
		7.3.4. Toffoli gate
		7.3.5. Deutsch’s problem
		7.3.6. Different superpositions
8. Application of Representation Theory
	8.1. Linear Transformations on the Same “Surface”
	8.2. Raising and Lowering Operators
	8.3. Basis Vectors in the 3D Case
	8.4. Basis Vectors in the 4D Case
9. A Few Concluding Words
	9.1. Infinity
	9.2. Completeness
	9.3. Summary
Glossary
Bibliography