عنوان

Formal Methods :

9401032696

9789401032698

b594498

Formal Methods :

[Book]

an Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logi

by Evert W. Beth.

Dordrecht

Springer Netherlands

1970

(188 pages).

Synthese Library, A Series of Monographs on the Recent Development of Symbolic Logic, Significs, Sociology of Language, Sociology of Science and of Knowledge, Statistics of Language and Related Fields, 4.

I. Purely Implicational Logic.- 1. Introduction.- 2. Deduction-Theoretic Approach.- 3. Semantic Approach.- 4. Axiomatic Approach.- 5. Completeness.- II. Full Sentential Logic.- 6. Introduction.- 7. Introduction of Further Sentential Connectives.- III. Theory of Quantification, Equality, and Functionality.- 8. Notation.- 9. Reduction Schemata.- 10. Axiomatic Method.- 11. Weak Completeness Theorems.- 12. Equality.- 13. Functionality.- IV. Completeness of Elementary Logic.- 14. Introduction.- 15. Quantification Theory.- 16. Theory of Equality and Functionality.- V. The Formalization of Arithmetic and its Limitations.- 17. An Axiom System for Arithmetic.- 18. Syntactic Incompleteness.- 19. Semantic Incompleteness.- 20. Logic of Higher Order.- VI. The Theory of Definition.- 21. Introduction.- 22. Definability of Primitive Notions.- 23. Padoa's Method.- 24. Definition-Theoretic Incompleteness.- VII. On Machines Which Prove Theorems.- 25. Introduction - Computation and Formal Deduction.- 26. Formal Deduction and Computing Machines.- 27. The Subformula Principle.- 28. Semantic Tableaux and Natural Deduction.- 29. Complications.- 30. Introduction of New Individual Parameters.- 31. Types of Logical Problems.- 32. Concluding Remarks.- Appendix: Supplementary Explanations.- 33. Formal Description of Deduction by Closed Semantic Tableaux.- 34. Independence.- 35. Intuitionistic Logic and Minimal Calculus.- 37. Elementary Logic with Equality and Terms.- 39. Semantic Rules for Quantification Theory.- 40. Deduction-Theoretic Treatment of the Theory of Quantification.- 41. Numerical Computation.- 42. The Interpolation Theorem of Craig-Lyndon.- List of Schemata and Axioms.- (A) Sources.- (B) Recommended Reading.- (C) Periodicals.- Index of Authors and Subjects.

Logic.

Philosophy (General)

by Evert W. Beth.

Evert W Beth

[Book]

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