1st Edition

Mechanical Logic in Three-Dimensional Space




ISBN 9789814411509
Published October 24, 2013 by Jenny Stanford Publishing
400 Pages 8 Color & 23 B/W Illustrations

USD $160.00

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Book Description

The book explores how build a mechanical inferences by making use of arithmetic operations on a string of numbers representing statements. In this way logic is reduced to a branch of the combinatory calculus. It covers the field of traditional logic by showing that any kind of inference can be mechanically reduced to three-variables and two-premise inferences. Meriological inferences can also be easily treated in this way. The book covers the following subjects: structural description of space; three-variable inferences through products, sums, subtractions, and divisions; generalization to n variables; relations; and applications.

Table of Contents

Structural Description
One-Dimensional Space
Two-Dimensional Space
Three-Dimensional Space

Product Inferences
Introduction
Derivation of Classical Inferences Through Products
Extension of Classical Inferences Through Products
Derivation of the Inferences of the First Mixed Mode Through Products
Derivation of the Inferences of the Second Mixed Mode Through Products

Sums
Introduction
Classical Inferences Through Sums
Extension of Classical Derivation Through Sums
First Mixed Mode Through Sums
Second Mixed Mode Through Sums

Subtractions
Introduction
Classical Inferences Through Subtractions
Extension of Classical Inferences Through Subtraction
First Mixed Mode Through Subtractions
Second Mixed Mode Through Subtractions

Divisions
Introduction
Classical Derivations Through Divisions
Extension of Classical Derivations Through Divisions
Inferences of the First Mixed Mode Though Divisions
Inferences of the Second Mixed Mode Through Divisions

Assessment of All the Previous Inferences
General Considerations
Product Inferences
Sum Inferences
Subtraction Inferences
Division Inferences
Simplified Summary of the Previous Inferences

Generalized Representation and Structural Relations
Subtractions
Divisions
Final Considerations

Generalized Inferences
The Basic Forms of the Previous and New Inferences
The Most General Forms of Closed Inference
The Results of All the Derivations
Cycles of Inferences
Open Inferences With Two and More Variables
Mereological Inferences and Related Ones
Open Inferences and Relations
Why Three?

Applications
Artificial Intelligence
Classical Computing
Quantum Computing: Raising and Lowering Operators

Conclusions
Bibliography
Author Index
Subject Index

Color Plate Section

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