Mechanical Logic in Three-Dimensional Space

Mechanical Logic in Three-Dimensional Space

by Gennaro Auletta
Released April 2016
Publisher(s): Jenny Stanford Publishing
ISBN: 9789814411516

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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

  1. Front Cover
  2. Contents
  3. Introduction
  4. Part I Logical Spaces
    1. Chapter 1 Structural Description (1/12)
    2. Chapter 1 Structural Description (2/12)
    3. Chapter 1 Structural Description (3/12)
    4. Chapter 1 Structural Description (4/12)
    5. Chapter 1 Structural Description (5/12)
    6. Chapter 1 Structural Description (6/12)
    7. Chapter 1 Structural Description (7/12)
    8. Chapter 1 Structural Description (8/12)
    9. Chapter 1 Structural Description (9/12)
    10. Chapter 1 Structural Description (10/12)
    11. Chapter 1 Structural Description (11/12)
    12. Chapter 1 Structural Description (12/12)
  5. Part II "Closed" Inferences
    1. Chapter 2 Product Inferences (1/13)
    2. Chapter 2 Product Inferences (2/13)
    3. Chapter 2 Product Inferences (3/13)
    4. Chapter 2 Product Inferences (4/13)
    5. Chapter 2 Product Inferences (5/13)
    6. Chapter 2 Product Inferences (6/13)
    7. Chapter 2 Product Inferences (7/13)
    8. Chapter 2 Product Inferences (8/13)
    9. Chapter 2 Product Inferences (9/13)
    10. Chapter 2 Product Inferences (10/13)
    11. Chapter 2 Product Inferences (11/13)
    12. Chapter 2 Product Inferences (12/13)
    13. Chapter 2 Product Inferences (13/13)
    14. Chapter 3 Sums (1/9)
    15. Chapter 3 Sums (2/9)
    16. Chapter 3 Sums (3/9)
    17. Chapter 3 Sums (4/9)
    18. Chapter 3 Sums (5/9)
    19. Chapter 3 Sums (6/9)
    20. Chapter 3 Sums (7/9)
    21. Chapter 3 Sums (8/9)
    22. Chapter 3 Sums (9/9)
    23. Chapter 4 Subtractions (1/8)
    24. Chapter 4 Subtractions (2/8)
    25. Chapter 4 Subtractions (3/8)
    26. Chapter 4 Subtractions (4/8)
    27. Chapter 4 Subtractions (5/8)
    28. Chapter 4 Subtractions (6/8)
    29. Chapter 4 Subtractions (7/8)
    30. Chapter 4 Subtractions (8/8)
    31. Chapter 5 Divisions (1/8)
    32. Chapter 5 Divisions (2/8)
    33. Chapter 5 Divisions (3/8)
    34. Chapter 5 Divisions (4/8)
    35. Chapter 5 Divisions (5/8)
    36. Chapter 5 Divisions (6/8)
    37. Chapter 5 Divisions (7/8)
    38. Chapter 5 Divisions (8/8)
  6. Part III Generalizations And Applications
    1. Chapter 6 Assessment Of All The Previous Inferences (1/5)
    2. Chapter 6 Assessment Of All The Previous Inferences (2/5)
    3. Chapter 6 Assessment Of All The Previous Inferences (3/5)
    4. Chapter 6 Assessment Of All The Previous Inferences (4/5)
    5. Chapter 6 Assessment Of All The Previous Inferences (5/5)
    6. Chapter 7 Generalized Representation And Structural Relations (1/2)
    7. Chapter 7 Generalized Representation And Structural Relations (2/2)
    8. Chapter 8 Generalized Inferences (1/15)
    9. Chapter 8 Generalized Inferences (2/15)
    10. Chapter 8 Generalized Inferences (3/15)
    11. Chapter 8 Generalized Inferences (4/15)
    12. Chapter 8 Generalized Inferences (5/15)
    13. Chapter 8 Generalized Inferences (6/15)
    14. Chapter 8 Generalized Inferences (7/15)
    15. Chapter 8 Generalized Inferences (8/15)
    16. Chapter 8 Generalized Inferences (9/15)
    17. Chapter 8 Generalized Inferences (10/15)
    18. Chapter 8 Generalized Inferences (11/15)
    19. Chapter 8 Generalized Inferences (12/15)
    20. Chapter 8 Generalized Inferences (13/15)
    21. Chapter 8 Generalized Inferences (14/15)
    22. Chapter 8 Generalized Inferences (15/15)
    23. Chapter 9 Applications (1/4)
    24. Chapter 9 Applications (2/4)
    25. Chapter 9 Applications (3/4)
    26. Chapter 9 Applications (4/4)
    27. Chapter 10 Conclusions
  7. Bibliography
  8. Back Cover

Product information

  • Title: Mechanical Logic in Three-Dimensional Space
  • Author(s): Gennaro Auletta
  • Release date: April 2016
  • Publisher(s): Jenny Stanford Publishing
  • ISBN: 9789814411516