Error Logic: Paving Pathways for Intelligent Error Identification and Management: Programming and Interfacing

Description

This book offers a brand-new theoretical system and relevant tools for intelligently identifying errors in the decision-making process, investigating the complexities and erring mechanisms of dysfunctional socioeconomic systems, and therefore helping design error-proof systems. The error logic is invented to pioneer a new branch for the field of logic, which can be applied to various fields including mathematics, philosophy, computer science, artificial intelligence, linguistics, management science, and systems science. Researchers, postgraduates, and undergraduates in relevant fields can use it as a reference for enhancing their understanding of the tempo-spatial dynamics and transformation of errors in complicated systems. The manuscript also provides vivid and thought-provoking examples and applications to help readers understand how to apply the concepts and theory in real socioeconomic systems. Contents Acronyms 1 Preface References 2 Short Introduction on the Logic 2.1 Major Theories in Modern Logic 2.1.1 Origin of Mathematical Logic 2.1.2 Contents of Mathematical Logic 2.1.3 Research History of Mathematical Logic 2.1.4 Development of Mathematical Logic 2.1.5 Research Status of Mathematical Logic 2.1.6 Formalism of Dialectical Logic in China 2.2 Error Logical System 2.2.1 Existential Quantifiers 3 Error Sets 3.1 Concepts of Error Sets 3.1.1 Error Sets 3.1.2 Operations of Error Sets and Their Laws 3.2 Transformation of Error Sets 3.2.1 Definition of Transformation of Error Sets 3.2.2 Transformation Operations of Error Sets 3.2.3 Types and Operation Rules of Transformation 3.2.4 Transformation and Elimination of Errors 3.3 Classic Error Set 3.3.1 Concepts of Classic Error Set 3.3.2 Categories of Classic Error Set 3.3.3 Operations of Classic Error Set and Their Laws 3.4 Fuzzy Error Set 3.4.1 Concepts of Fuzzy Error Set 3.4.2 Operations of Fuzzy Error Set and Their Laws 3.4.3 Error Set with Critical Points 3.5 Multivariate Error Set 3.5.1 Concepts 3.5.2 Binary Error Set 3.5.3 Types of Transformation on Binary Error Set and Their Laws of Operations References 4 Transformation Connectives in Error Logic 4.1 Similarity Transformation Connectives in Error Logic 4.1.1 Basic Concepts 4.1.2 Basic Operations 4.1.3 Similarity Transformation Connectives in Error Logic 4.1.4 Characteristics of Domain Similarity Transformation Connectives in Error Logic 4.1.5 Characteristics of Thing Similarity Transformation Connectives in Error Logic 4.1.6 Characteristics of Property Similarity Transformation Connectives in Error Logic 4.1.7 Characteristics of Spatial Similarity Transformation Connectives in Error Logic 4.1.8 Characteristics of Property (or Attribute) Value Similarity Transformation Connectives in Error Logic 4.1.9 Characteristics of Error Value Similarity Transformation Connectives in Error Logic 4.1.10 Characteristics of Rule Similarity Transformation Connectives in Error Logic 4.1.11 Characteristics of Error Function Similarity Transformation Connectives in Error Logic 4.1.12 Characteristics of Temporal Similarity Transformation Connectives in Error Logic 4.1.13 Characteristics of Combination Similarity Transformation Connectives in Error Logic 4.2 Decomposition Transformation Connectives in Error Logic 4.2.1 Concepts of Decomposition Transformation Connectives in Error Logic 4.2.2 Domain Decomposition Transformation Connective in Error Logic 4.2.3 Thing Decomposition Transformation Connective in Error Logic 4.2.4 Spatial Decomposition Transformation Connective in Error Logic 4.2.5 Property Decomposition Transformation Connective in Error Logic 4.2.6 Property (or Attribute) Value Decomposition Transformation Connective in Error Logic 4.2.7 Error Value Decomposition Transformation Connective in Error Logic 4.2.8 Error Function Decomposition Transformation Connective in Error Logic 4.2.9 Time Decomposition Transformation Connective in Error Logic 4.2.10 Rule Decomposition Transformation Connective in Error Logic 4.2.11 Overall Decomposition Transformation Connectives in Error Logic 4.3 Displacement Transformation Connectives in Error Logic 4.3.1 Concepts of Displacement Transformation Connective in Error Logic 4.3.2 Domain Displacement Transformation Connective in Error Logic 4.3.3 Thing Displacement Transformation Connective in Error Logic 4.4 Increase Transformation Connectives in Error Logic 4.4.1 Increase Transformation Connectives in Error Logic 4.4.2 Characteristics of Error Value Increase Transformation Connective in Error Logic 4.5 Destruction Transformation Connectives in Error Logic 4.5.1 Concept of Destruction Transformation Connectives in Error Logic 4.5.2 Principles for Destruction Transformation in Error Logic 4.5.3 Approaches of Destruction Transformation in Error Logic 4.5.4 Hierarchy of Destruction Transformation in Error Logic 4.5.5 Characteristics of Domain Destruction Transformation Connective Th in Error Logic 4.5.6 Thing Destruction Transformation Connectives in Error Logic 4.5.7 Property Destruction Transformation Connectives in Error Logic 4.5.8 Engenderment Transformation Connectives in Error Logic 5 Mathematical Error Propositional Logic 5.1 Concept of Mathematical Error Propositional Logic 5.2 Error Logical System 5.2.1 Existential Quantifiers 5.3 Atomic Propositions 5.4 Basic Operations 5.5 Compound Proposition 5.5.1 Atomic Proposition 5.5.2 Error Logical Compound Proposition 5.6 Basic Rules for Error Logical Reasoning 5.6.1 Axiom Set 5.6.2 Reasoning Rules 5.7 Forms of Error Logical Proposition 5.8 Error Predicate Logic 5.8.1 Forms of Error Predicate Logic 5.8.2 Form Language of Error Predicate Logic 5.9 Semantic Explanation of Error Predicate Logical Expression 6 Applications of Error Logic 6.1 Applying Error Matrix Equation to Investigate Urban Traffic Congestion 6.1.1 Problem Statement 6.1.2 Method for Finding Solutions 6.1.3 Modeling Error-elimination for a Urban Traffic Intersection 6.1.4 Flowchart Representing Process of Finding Solutions 6.1.5 Modeling Building and Analysis 6.2 Computerized Error Logical Reasoning 6.2.1 Error Theory-Based Expert System Structure 6.2.2 Application Case 6.3 Knowledge Representation Model for Ecological Civilization Indicators 6.3.1 Decomposition Transformation Connectives in Error Logic 6.3.2 Principles and Types for Decomposition Transformation in Error Logic 6.3.3 Knowledge Representation Model for Ecological Civilization Performance Indicators 6.4 Error Transmission in a System 6.4.1 Critical Factors for Error Transmission in a System 6.4.2 Expression Form for a System 6.4.3 Error Transmission Function in a System 6.4.4 Application Example for Concept of Error Transmission 6.5 Application of Error Logic in Decision Support System for Nanquan Referees 6.5.1 Description on the Error Object of Nanquan in Error Logical Matrix 6.5.2 Error Logic-based Object System of Nanquan Movement Rules 6.5.3 Computer Vision-based Error Identification Model for Optional Nanquan 6.5.4 Application of Computer Vision-based Error Identification Model for Optional Nanquan 6.5.5 Summary for the Application Glossary