Skip to Content

Mechanical Logic in Three-Dimensional Space

By Gennaro Auletta

Pan Stanford – 2013 – 400 pages

Purchasing Options:

  • Add to CartHardback: $149.95
    9789814411509
    October 23rd 2013

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.

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

Name: Mechanical Logic in Three-Dimensional Space (Hardback)Pan Stanford 
Description: By Gennaro Auletta. 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...
Categories: Robotics, Computer Engineering, Set Theory