Mechanical Logic in Three-Dimensional Space

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 DescriptionOne-Dimensional SpaceTwo-Dimensional SpaceThree-Dimensional SpaceProduct InferencesIntroductionDerivation of Classical Inferences Through Products Extension of Classical Inferences Through ProductsDerivation of the Inferences of the First Mixed Mode Through ProductsDerivation of the Inferences of the Second Mixed Mode Through ProductsSumsIntroductionClassical Inferences Through SumsExtension of Classical Derivation Through Sums First Mixed Mode Through Sums Second Mixed Mode Through Sums SubtractionsIntroduction Classical Inferences Through Subtractions Extension of Classical Inferences Through Subtraction First Mixed Mode Through Subtractions Second Mixed Mode Through Subtractions DivisionsIntroduction 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 InferencesGeneral Considerations Product Inferences Sum Inferences Subtraction Inferences Division Inferences Simplified Summary of the Previous Inferences Generalized Representation and Structural RelationsSubtractionsDivisionsFinal Considerations Generalized InferencesThe 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 RelationsWhy Three? ApplicationsArtificial IntelligenceClassical Computing Quantum Computing: Raising and Lowering Operators ConclusionsBibliographyAuthor IndexSubject IndexColor Plate Section