1st Edition

Mechanical Logic in Three-Dimensional Space

By Gennaro Auletta Copyright 2013
    400 Pages 8 Color & 23 B/W Illustrations
    by Jenny Stanford Publishing

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    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.

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

    Product Inferences
    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

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

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

    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
    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?

    Artificial Intelligence
    Classical Computing
    Quantum Computing: Raising and Lowering Operators

    Author Index
    Subject Index

    Color Plate Section


    Gennaro Auletta