Combinatory Logic

Name: Combinatory Logic
Brand: Elsevier
Price: 215.0 EUR
Availability: OnlineOnly

Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

435 Seiten

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978-0-08-095742-5 (ISBN)

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Inhalt

Front Cover
Combinatory Logic, Volume 22
Copyright Page
Table of Contents
Preface
Explanation of Notations
Introduction
A. The Analysis of Substitution
B. The Russell Paradox
C. Plan of the Work
D. Historical Sketch
Chapter 1. Formal Systems
A. The Approach to Formal Systems
B. Definition of a Formal System
C. Philosophy of Formal Systems
D. Linguistic Aspects of a Formal System
E. Special Forms of Formal Systems
S. Supplementary Topics
Chapter 2. Epitheory
A. The Nature of Epitheory
B. Techniques of Induction
C. Variables
D. Replacement and Monotone Relations
E. Theory of Definition
S. Supplementary Topics
Chapter 3. Lambda-Conversion
A. Variables and Functions in Mathematics
B. Functional Abstraction
C. Morphology of a Formal ?-Applicative System
D. Theoretical Rules of the Calculuses of Lambda-Conversion
E. Substitution Prefixes
S. Supplementary Topics
Chapter 4. The Church-Rosser Theorem
A. General Formulation
B. Property (D)
C. Property (E)
D. Extension to Include ?-Conversion
E. The Second Church-Rosser Theorem
F. Theorems on Order
S. Supplementary Topics
Chapter 5. Intuitive Theory of Combinators
A. Preliminary Discussion
B. Interdefinability of Simple Combinators
C. Terminology and Notation
D. Properties of B
E. Combinators Related to S
F. Theorems on Order of Combinators
G. Paradoxical Combinators
H. Definitional Independence of Combinators
S. Supplementary Topics
Chapter 6. Synthetic Theory of Combinators
A. Analysis of Combinatorial Completeness
B. Basic Properties of H
C. The Combinatory Axioms
D. Theory of the Substitution Prefix
E. Equivalence of H and Lambda-Conversion
F. Theory of Strong Reduction
S. Supplementary Topics
Chapter 7. Logistic Foundations
A. Preliminaries
B. The Combinatory Rules
C. The Systems 2
D. The Systems K
E. Modifications and Generalizations
S. Supplementary Topics
Chapter 8. Introduction to Illative Combinatory Logic
A. The Russell Paradox
B. Alternative Explanations of the Paradox
C. The Notion of Functionality
D. Relations to Other Illative Concepts
E. Formal Preliminaries
S. Supplementary Topics
Chapter 9. The Basic Theory of Functionality
A. Preliminaries
B. The Subject-Construction Theorem
C. Thc Subject-Conversion Theorems
D. The Stratification Theorem and Its Consequences
E. Analogies with Propositional Algebra
F. Inferential Forms of Functionality
S. Supplementary Topics
Chapter 10. The Stronger Theories of Functionality
A. Preliminaries
B. General Properties of Deductions
C. FR-Deductions
D. The Restricted Theories
E. Finite Formulation
Appendix A. List of Basic Constants
Appendix B. List of Properties of Relations
Bibliography
Index

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